A368166 Expansion of e.g.f. -log(1 + x^3/6 * log(1 - x)).

0, 0, 0, 0, 4, 10, 40, 210, 1904, 15120, 132600, 1293600, 14673120, 178738560, 2341182480, 32915282400, 499117301760, 8075042976000, 138689356915200, 2519863488979200, 48354005826489600, 976893364144857600, 20721305503846886400, 460363370406207206400

Offset

0,5

Comments

This sequence is different from A351493.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).

a(0) = a(1) = a(2) = a(3) = 0; a(n) = n!/(6*(n-3)) + Sum_{k=4..n-1} k!/(6*(k-3)) * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025

Prog

(PARI) a(n) = n!*sum(k=1, n\4, (k-1)!*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Crossrefs

Cf. A052804, A368165.

Cf. A351493, A351506.

Sequence in context: A222367 A356913 A351493 * A351506 A355995 A356753

Adjacent sequences: A368163 A368164 A368165 * A368167 A368168 A368169

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2023

Status

approved