OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..450
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(k,3)/k!.
a(0) = 0; a(n) = n * a(n-1) + binomial(n,3).
E.g.f.: x^3/6 * exp(x)/(1-x).
G.f.: (1/6) * Sum_{k>=3} k! * x^k/(1-x)^(k+1).
MATHEMATICA
Table[n!/6 Sum[1/k!, {k, 0, n-3}], {n, 0, 30}] (* Harvey P. Dale, Apr 02 2023 *)
PROG
(PARI) a(n) = n!/6*sum(k=0, n-3, 1/k!);
(PARI) a(n) = n!*sum(k=0, n, binomial(k, 3)/k!);
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(x^3/6*exp(x)/(1-x))))
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=3, N, k!*x^k/(1-x)^(k+1))/6))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 30 2022
STATUS
approved