A336197 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^5 * a(k).

1, 1, 33, 8263, 8718945, 28076306251, 224968772934303, 3896175006605313013, 131557135159637950535265, 8004845815916146011992853811, 824857614282973828473497207276283, 136888961901974254918775560412316183913, 35099479542762449254288789631427310686677535

Offset: 0

Author

Ilya Gutkovskiy, Jul 11 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..120

Crossrefs

Column k=5 of A326322.

Cf. A000670, A102221, A336195, A336196.

Programs

Mathematica

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

Formula

a(n) = (n!)^5 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^5).