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

0,3

Links

Table of n, a(n) for n=0..14.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A368770, A368771, A368772.

Cf. A002627, A066998.

Cf. A217284, A271574.

Sequence in context: A167005 A112028 A375178 * A329305 A183235 A359732

Adjacent sequences: A368766 A368767 A368768 * A368770 A368771 A368772

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2024

Status

approved