History of Partial Bell polynomials $B_{n,k}$

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compare when who what
2026-08-26 18:38 bmatschke the partial Bell polynomials, variables indexed from one current reviewed
2026-08-26 18:38 bmatschke checking that this table can be written to
2026-08-26 18:38 bmatschke with claude-opus-5 the range the six-variable search key allows
2026-08-26 18:35 bmatschke with claude-opus-5 proposed from bell.yaml

What changed between 2026-08-26 18:38 and 2026-08-26 18:38

from line 72 (115 lines, 112 more than before) @@ -72,3 +72,115 @@
       \ range(n - k + 1)])\n    return R(p.subs({g: R.gen(i) for i, g in enumerate(p.parent().gens())}))\n\       \npartial_bell(17, 8)              # past the end of this table"-Numbers: []+Numbers:+- params:+    n: '1'+    k: '1'+  number: x1+- params:+    n: '2'+    k: '1'+  number: x2+- params:+    n: '2'+    k: '2'+  number: x1^2+- params:+    n: '3'+    k: '1'+  number: x3+- params:+    n: '3'+    k: '2'+  number: 3*x1*x2+- params:+    n: '3'+    k: '3'+  number: x1^3+- params:+    n: '4'+    k: '1'+  number: x4+- params:+    n: '4'+    k: '2'+  number: 3*x2^2 + 4*x1*x3+- params:+    n: '4'+    k: '3'+  number: 6*x1^2*x2+- params:+    n: '4'+    k: '4'+  number: x1^4+- params:+    n: '5'+    k: '1'+  number: x5+- params:+    n: '5'+    k: '2'+  number: 10*x2*x3 + 5*x1*x4+- params:+    n: '5'+    k: '3'+  number: 15*x1*x2^2 + 10*x1^2*x3+- params:+    n: '5'+    k: '4'+  number: 10*x1^3*x2+- params:+    n: '5'+    k: '5'+  number: x1^5+- params:+    n: '6'+    k: '1'+  number: x6+- params:+    n: '6'+    k: '2'+  number: 10*x3^2 + 15*x2*x4 + 6*x1*x5+- params:+    n: '6'+    k: '3'+  number: 15*x2^3 + 60*x1*x2*x3 + 15*x1^2*x4+- params:+    n: '6'+    k: '4'+  number: 45*x1^2*x2^2 + 20*x1^3*x3+- params:+    n: '6'+    k: '5'+  number: 15*x1^4*x2+- params:+    n: '6'+    k: '6'+  number: x1^6+- params:+    n: '7'+    k: '1'+  number: x7+- params:+    n: '7'+    k: '2'+  number: 35*x3*x4 + 21*x2*x5 + 7*x1*x6+- params:+    n: '7'+    k: '3'+  number: 105*x2^2*x3 + 70*x1*x3^2 + 105*x1*x2*x4 + 21*x1^2*x5+- params:+    n: '7'+    k: '4'+  number: 105*x1*x2^3 + 210*x1^2*x2*x3 + 35*x1^3*x4+- params:+    n: '7'+    k: '5'+  number: 105*x1^3*x2^2 + 35*x1^4*x3+- params:+    n: '7'+    k: '6'+  number: 21*x1^5*x2+- params:+    n: '7'+    k: '7'+  number: x1^7 

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