A337678 a(0) = 1; a(n) = -(n!)^5 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^5.

1, -1, 31, -7322, 7281664, -22105862624, 166969429228448, -2726003940127256256, 86768429205346333655040, -4977000682976771751013908480, 483455102073887625685155978412032, -75632981854199587114694850276377296896, 18281294958403743105166278735321854559387648

Offset: 0

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

• sign

Crossrefs

Cf. A006252, A074706, A212858, A336261, A337676, A337677.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -(n!)^5 Sum[a[k]/(k! (n - k))^5, {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]
nmax = 12; CoefficientList[Series[1/(1 + PolyLog[5, x]), {x, 0, nmax}], x] Range[0, nmax]!^5

PARI

a(n)={n!^5*polcoef(1/(1 + polylog(5,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^5 = 1 / (1 + polylog(5,x)).