OFFSET
0,6
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..450
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(k,4)/k!.
a(0) = 0; a(n) = n * a(n-1) + binomial(n,4).
E.g.f.: x^4/24 * exp(x)/(1-x).
G.f.: (1/24) * Sum_{k>=4} k! * x^k/(1-x)^(k+1).
PROG
(PARI) a(n) = n!/24*sum(k=0, n-4, 1/k!);
(PARI) a(n) = n!*sum(k=0, n, binomial(k, 4)/k!);
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(x^4/24*exp(x)/(1-x))))
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=4, N, k!*x^k/(1-x)^(k+1))/24))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 30 2022
STATUS
approved