A368769 a(n) = (n!)^3 * Sum_{k=1..n} 1/(k!)^3.

0, 1, 9, 244, 15617, 1952126, 421659217, 144629111432, 74050105053185, 53982526583771866, 53982526583771866001, 71850742883000353647332, 124158083701824611102589697, 272775309892908670592389564310, 748495450346141392105516964466641

Offset: 0

Author

Seiichi Manyama, Jan 04 2024

Keywords

• nonn

Crossrefs

Cf. A368770, A368771, A368772.

Cf. A002627, A066998.

Cf. A217284, A271574.

Programs

Mathematica

Table[(n!)^3 Sum[1/(k!)^3,{k,n}],{n,0,20}] (* Harvey P. Dale, May 11 2025 *)

PARI

a(n) = n!^3*sum(k=1, n, 1/k!^3);

Formula

a(0) = 0; a(n) = n^3 * a(n-1) + 1.

a(n) = A217284(n) - (n!)^3.

a(n) ~ (A271574 - 1) * (n!)^3. - Vaclav Kotesovec, Jan 05 2024