Where each entry of Hermite polynomials in probabilist's convention came from

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51 entries.

n value last changed by
0 1 2026-08-09flattening
1 x 2026-08-09flattening
2 x^2 - 1 2026-08-09flattening
3 x^3 - 3*x 2026-08-09flattening
4 x^4 - 6*x^2 + 3 2026-08-09flattening
5 x^5 - 10*x^3 + 15*x 2026-08-09flattening
6 x^6 - 15*x^4 + 45*x^2 - 15 2026-08-09flattening
7 x^7 - 21*x^5 + 105*x^3 - 105*x 2026-08-09flattening
8 x^8 - 28*x^6 + 210*x^4 - 420*x^2 + 105 2026-08-09flattening
9 x^9 - 36*x^7 + 378*x^5 - 1260*x^3 + 945*x 2026-08-09flattening
10 x^10 - 45*x^8 + 630*x^6 - 3150*x^4 + 4725*x^2 - 945 2026-08-09flattening
11 x^11 - 55*x^9 + 990*x^7 - 6930*x^5 + 17325*x^3 - 10395*x 2026-08-09flattening
12 x^12 - 66*x^10 + 1485*x^8 - 13860*x^6 + 51975*x^4 - 62370*x^2 + 10395 2026-08-09flattening
13 x^13 - 78*x^11 + 2145*x^9 - 25740*x^7 + 135135*x^5 - 270270*x^3 + 135… 2026-08-09flattening
14 x^14 - 91*x^12 + 3003*x^10 - 45045*x^8 + 315315*x^6 - 945945*x^4 + 94… 2026-08-09flattening
15 x^15 - 105*x^13 + 4095*x^11 - 75075*x^9 + 675675*x^7 - 2837835*x^5 + … 2026-08-09flattening
16 x^16 - 120*x^14 + 5460*x^12 - 120120*x^10 + 1351350*x^8 - 7567560*x^6… 2026-08-09flattening
17 x^17 - 136*x^15 + 7140*x^13 - 185640*x^11 + 2552550*x^9 - 18378360*x^… 2026-08-09flattening
18 x^18 - 153*x^16 + 9180*x^14 - 278460*x^12 + 4594590*x^10 - 41351310*x… 2026-08-09flattening
19 x^19 - 171*x^17 + 11628*x^15 - 406980*x^13 + 7936110*x^11 - 87297210*… 2026-08-09flattening
20 x^20 - 190*x^18 + 14535*x^16 - 581400*x^14 + 13226850*x^12 - 17459442… 2026-08-09flattening
21 x^21 - 210*x^19 + 17955*x^17 - 813960*x^15 + 21366450*x^13 - 33331662… 2026-08-09flattening
22 x^22 - 231*x^20 + 21945*x^18 - 1119195*x^16 + 33575850*x^14 - 6110804… 2026-08-09flattening
23 x^23 - 253*x^21 + 26565*x^19 - 1514205*x^17 + 51482970*x^15 - 1081142… 2026-08-09flattening
24 x^24 - 276*x^22 + 31878*x^20 - 2018940*x^18 + 77224455*x^16 - 1853386… 2026-08-09flattening
25 x^25 - 300*x^23 + 37950*x^21 - 2656500*x^19 + 113565375*x^17 - 308897… 2026-08-09flattening
26 x^26 - 325*x^24 + 44850*x^22 - 3453450*x^20 + 164038875*x^18 - 501958… 2026-08-09flattening
27 x^27 - 351*x^25 + 52650*x^23 - 4440150*x^21 + 233107875*x^19 - 797228… 2026-08-09flattening
28 x^28 - 378*x^26 + 61425*x^24 - 5651100*x^22 + 326351025*x^20 - 124013… 2026-08-09flattening
29 x^29 - 406*x^27 + 71253*x^25 - 7125300*x^23 + 450675225*x^21 - 189283… 2026-08-09flattening
30 x^30 - 435*x^28 + 82215*x^26 - 8906625*x^24 + 614557125*x^22 - 283925… 2026-08-09flattening
31 x^31 - 465*x^29 + 94395*x^27 - 11044215*x^25 + 828316125*x^23 - 41912… 2026-08-09flattening
32 x^32 - 496*x^30 + 107880*x^28 - 13592880*x^26 + 1104421500*x^24 - 609… 2026-08-09flattening
33 x^33 - 528*x^31 + 122760*x^29 - 16613520*x^27 + 1457836380*x^25 - 874… 2026-08-09flattening
34 x^34 - 561*x^32 + 139128*x^30 - 20173560*x^28 + 1906401420*x^26 - 123… 2026-08-09flattening
35 x^35 - 595*x^33 + 157080*x^31 - 24347400*x^29 + 2471261100*x^27 - 173… 2026-08-09flattening
36 x^36 - 630*x^34 + 176715*x^32 - 29216880*x^30 + 3177335700*x^28 - 240… 2026-08-09flattening
37 x^37 - 666*x^35 + 198135*x^33 - 34871760*x^31 + 4053842100*x^29 - 329… 2026-08-09flattening
38 x^38 - 703*x^36 + 221445*x^34 - 41410215*x^32 + 5134866660*x^30 - 446… 2026-08-09flattening
39 x^39 - 741*x^37 + 246753*x^35 - 48939345*x^33 + 6459993540*x^31 - 600… 2026-08-09flattening
40 x^40 - 780*x^38 + 274170*x^36 - 57575700*x^34 + 8074991925*x^32 - 801… 2026-08-09flattening
41 x^41 - 820*x^39 + 303810*x^37 - 67445820*x^35 + 10032565725*x^33 - 10… 2026-08-09flattening
42 x^42 - 861*x^40 + 335790*x^38 - 78686790*x^36 + 12393169425*x^34 - 13… 2026-08-09flattening
43 x^43 - 903*x^41 + 370230*x^39 - 91446810*x^37 + 15225893865*x^35 - 18… 2026-08-09flattening
44 x^44 - 946*x^42 + 407253*x^40 - 105885780*x^38 + 18609425835*x^36 - 2… 2026-08-09flattening
45 x^45 - 990*x^43 + 446985*x^41 - 122175900*x^39 + 22633085475*x^37 - 3… 2026-08-09flattening
46 x^46 - 1035*x^44 + 489555*x^42 - 140502285*x^40 + 27397945575*x^38 - … 2026-08-09flattening
47 x^47 - 1081*x^45 + 535095*x^43 - 161063595*x^41 + 33018036975*x^39 - … 2026-08-09flattening
48 x^48 - 1128*x^46 + 583740*x^44 - 184072680*x^42 + 39621644370*x^40 - … 2026-08-09flattening
49 x^49 - 1176*x^47 + 635628*x^45 - 209757240*x^43 + 47352696930*x^41 - … 2026-08-09flattening
50 x^50 - 1225*x^48 + 690900*x^46 - 238360500*x^44 + 56372258250*x^42 - … 2026-08-09flattening