A336260 a(0) = 1; a(n) = (n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4.

1, 1, 17, 1474, 404768, 271581776, 377987513392, 974814164752800, 4289222350867156992, 30232332223815625555968, 324796212685273837095714816, 5108947647642107040382284423168, 113818571142935411070742114448769024, 3492592855002964381945529723625305210880

Offset: 0

Author

Ilya Gutkovskiy, Jul 15 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..143

Crossrefs

Cf. A007840, A217145, A336196, A336258, A336259, A336261.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-i)/i^4, i=1..n))
    end:
a:= n-> n!^4*b(n):
seq(a(n), n=0..14);  # Alois P. Heinz, Jan 04 2024

Mathematica

a[0] = 1; a[n_] := a[n] = (n!)^4 Sum[a[k]/(k! (n - k))^4, {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
nmax = 13; CoefficientList[Series[1/(1 - PolyLog[4, x]), {x, 0, nmax}], x] Range[0, nmax]!^4

Formula

a(n) = (n!)^4 * [x^n] 1 / (1 - polylog(4,x)).

a(n) ~ (n!)^4 / (polylog(3,r) * r^n), where r = 0.93073451517099234709643607941... is the root of the equation polylog(4,r) = 1. - Vaclav Kotesovec, Jul 15 2020