euler-controls.json

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{
  "source": "https://numberdb.org/Euler_polynomials",
  "Title": "Euler polynomials $E_n$",
  "Numbers": {
    "0": "1",
    "1": "x - 1/2",
    "2": "x^2 - x",
    "3": "x^3 - 3/2*x^2 + 1/4",
    "4": "x^4 - 2*x^3 + x",
    "5": "x^5 - 5/2*x^4 + 5/2*x^2 - 1/2",
    "6": "x^6 - 3*x^5 + 5*x^3 - 3*x",
    "7": "x^7 - 7/2*x^6 + 35/4*x^4 - 21/2*x^2 + 17/8",
    "8": "x^8 - 4*x^7 + 14*x^5 - 28*x^3 + 17*x",
    "9": "x^9 - 9/2*x^8 + 21*x^6 - 63*x^4 + 153/2*x^2 - 31/2",
    "10": "x^10 - 5*x^9 + 30*x^7 - 126*x^5 + 255*x^3 - 155*x",
    "11": "x^11 - 11/2*x^10 + 165/4*x^8 - 231*x^6 + 2805/4*x^4 - 1705/2*x^2 + 691/4",
    "12": "x^12 - 6*x^11 + 55*x^9 - 396*x^7 + 1683*x^5 - 3410*x^3 + 2073*x",
    "13": "x^13 - 13/2*x^12 + 143/2*x^10 - 1287/2*x^8 + 7293/2*x^6 - 22165/2*x^4 + 26949/2*x^2 - 5461/2",
    "14": "x^14 - 7*x^13 + 91*x^11 - 1001*x^9 + 7293*x^7 - 31031*x^5 + 62881*x^3 - 38227*x",
    "15": "x^15 - 15/2*x^14 + 455/4*x^12 - 3003/2*x^10 + 109395/8*x^8 - 155155/2*x^6 + 943215/4*x^4 - 573405/2*x^2 + 929569/16",
    "16": "x^16 - 8*x^15 + 140*x^13 - 2184*x^11 + 24310*x^9 - 177320*x^7 + 754572*x^5 - 1529080*x^3 + 929569*x",
    "17": "x^17 - 17/2*x^16 + 170*x^14 - 3094*x^12 + 41327*x^10 - 376805*x^8 + 2137954*x^6 - 6498590*x^4 + 15802673/2*x^2 - 3202291/2",
    "18": "x^18 - 9*x^17 + 204*x^15 - 4284*x^13 + 67626*x^11 - 753610*x^9 + 5497596*x^7 - 23394924*x^5 + 47408019*x^3 - 28820619*x",
    "19": "x^19 - 19/2*x^18 + 969/4*x^16 - 5814*x^14 + 214149/2*x^12 - 1431859*x^10 + 26113581/2*x^8 - 74083926*x^6 + 900752361/4*x^4 - 547591761/2*x^2 + 221930581/4",
    "20": "x^20 - 10*x^19 + 285*x^17 - 7752*x^15 + 164730*x^13 - 2603380*x^11 + 29015090*x^9 - 211668360*x^7 + 900752361*x^5 - 1825305870*x^3 + 1109652905*x"
  }
}