A375557 Expansion of e.g.f. 1 / (1 - x * log(1 + x^2/2)).

1, 0, 0, 3, 0, -15, 180, 210, -5040, 39690, 207900, -3492720, 17463600, 324324000, -4411887480, 4013509500, 811847836800, -8695353466800, -58816449291600, 3057626682910800, -21599774075880000, -575128161628020000, 16098010485281524800, -26415290970898830000

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling1(k,n-2*k)/(2^k*k!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*log(1+x^2/2))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 1)/(2^k*k!));

Crossrefs

Cf. A375560.

Sequence in context: A013407 A013494 A375586 * A375167 A365972 A290580

Adjacent sequences: A375554 A375555 A375556 * A375558 A375559 A375560

Keyword

sign

Author

Seiichi Manyama, Aug 19 2024

Status

approved