A384836 a(n) = Sum_{k=0..floor(n/4)} |Stirling1(n,4*k)|.

1, 0, 0, 0, 1, 10, 85, 735, 6770, 67320, 724550, 8427650, 105615500, 1420941600, 20448793300, 313670857500, 5111631733000, 88224807112000, 1608190674259000, 30879323250633000, 623074177992110000, 13182400475167560000, 291842125111122170000, 6748135840840046510000

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2025

Keywords

• nonn

Crossrefs

Cf. A000142, A001710, A357828, A384837.

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

Programs

Mathematica

Table[Sum[Abs[StirlingS1[n, 4*k]], {k, 0, Floor[n/4]}], {n, 0, 30}]

PARI

a(n) = sum(k=0, n\4, abs(stirling(n, 4*k, 1))); \\ Michel Marcus, Jun 10 2025

Formula

a(n) ~ n!/4.