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A336197 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^5 * a(k). 6
1, 1, 33, 8263, 8718945, 28076306251, 224968772934303, 3896175006605313013, 131557135159637950535265, 8004845815916146011992853811, 824857614282973828473497207276283, 136888961901974254918775560412316183913, 35099479542762449254288789631427310686677535 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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

CROSSREFS

Column k=5 of A326322.

Cf. A000670, A102221, A336195, A336196.

Sequence in context: A099828 A099827 A269793 * A336261 A060705 A061687

Adjacent sequences:  A336194 A336195 A336196 * A336198 A336199 A336200

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 11 2020

STATUS

approved

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)