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

0,3

Links

Table of n, a(n) for n=0..12.

Formula

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

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

Prog

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

Crossrefs

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

Sequence in context: A263378 A306840 A212858 * A059384 A136676 A135811

Adjacent sequences: A337675 A337676 A337677 * A337679 A337680 A337681

Keyword

sign

Author

Ilya Gutkovskiy, Sep 15 2020

Status

approved