OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..381
FORMULA
E.g.f.: 1 / (1 - Sum_{k>=1} k^3*x^k/k!).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k^3 * a(n-k).
a(n) ~ n! / (r^(n+1) * exp(r) * (1 + 7*r + 6*r^2 + r^3)), where r = 0.33649177041401456061485914122406146158245451810028937972189... is the root of the equation exp(r)*r*(1 + 3*r + r^2) = 1. - Vaclav Kotesovec, Jun 29 2019
MATHEMATICA
nmax = 18; CoefficientList[Series[1/(1 - x (1 + 3 x + x^2) Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1 - x*(1 + 3*x + x^2)*exp(x)))) \\ Michel Marcus, Mar 10 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 29 2019
STATUS
approved