A355113 - OEIS

A355113

Expansion of e.g.f. 5 / (6 - 5*x - exp(5*x)).

1, 2, 13, 133, 1779, 29565, 589705, 13728695, 365295695, 10934634985, 363678872325, 13305294463275, 531030788556475, 22960273845453725, 1069101897816615425, 53336480697298243375, 2838300249311563302375, 160480124820425410172625, 9607441647405962075600125

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

a(n) ~ n! / ((1 + LambertW(exp(6))) * ((6 - LambertW(exp(6)))/5)^(n+1)). - Vaclav Kotesovec, Jun 19 2022

MATHEMATICA

nmax = 18; CoefficientList[Series[5/(6 - 5 x - Exp[5 x]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

CROSSREFS