A357480 a(n) = (n!/24) * Sum_{k=0..n-4} 1/k!.

0, 0, 0, 0, 1, 10, 75, 560, 4550, 41076, 410970, 4521000, 54252495, 705283150, 9873965101, 148109477880, 2369751647900, 40285778016680, 725144004303300, 13777736081766576, 275554721635336365, 5786649154342069650, 127306281395525539615, 2928044472097087420000

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

Column k=4 of A073107.

Cf. A000522, A007526, A038155, A357479.

Cf. A000332, A000475.

Sequence in context: A346842 A081017 A238987 * A271476 A025015 A228416

Adjacent sequences: A357477 A357478 A357479 * A357481 A357482 A357483

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 30 2022

Status

approved