A380339 Expansion of e.g.f. log(1 - x^2/2 * log(1 - x)).

0, 0, 0, 3, 6, 20, 0, -126, -1260, 3240, 108360, 1635480, 15075720, 119957760, 705729024, 6324040800, 130989549600, 3572031415680, 78736127656320, 1502102645890560, 25514633892182400, 423898384988494080, 7590291773745542400, 162254912688831916800, 4023271392778314673920

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (-1)^(k-1) * (k-1)! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).

a(0) = a(1) = a(2) = 0; a(n) = n!/(2*(n-2)) - Sum_{k=3..n-1} k!/(2*(k-2)) * binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = n!*sum(k=1, n\3, (-1)^(k-1)*(k-1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));

Crossrefs

Cf. A089064, A380338.

Cf. A368165, A368173.

Sequence in context: A326317 A306522 A290784 * A355605 A356912 A176993

Adjacent sequences: A380336 A380337 A380338 * A380340 A380341 A380342

Keyword

sign

Author

Seiichi Manyama, Jan 22 2025

Status

approved