A384837 a(n) = Sum_{k=0..floor(n/5)} |Stirling1(n,5*k)|.

1, 0, 0, 0, 0, 1, 15, 175, 1960, 22449, 269326, 3416985, 45997655, 657262606, 9959178229, 159758917956, 2707741441460, 48389066401764, 909877831207125, 17965423056654249, 371766710374672096, 8047954162682335066, 181941000229690525197, 4288430328840863166236, 105226297616943093770399

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2025

Keywords

• nonn

Crossrefs

Cf. A000142, A001710, A357828, A384836.

Cf. A000110, A024430, A143815, A365525, A365528.

Programs

Mathematica

Table[Sum[Abs[StirlingS1[n, 5*k]], {k, 0, Floor[n/5]}], {n, 0, 30}]

PARI

a(n) = sum(k=0, n\5, abs(stirling(n, 5*k, 1))); \\ Michel Marcus, Jun 10 2025

Formula

a(n) ~ n!/5.