A375167 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2)).

1, 0, 0, 3, 0, 15, 180, 210, 5040, 51030, 207900, 3991680, 42411600, 356756400, 6485398920, 80635054500, 1040690851200, 19440077857200, 291313362740400, 4914773560897200, 98182334033784000, 1763213788027692000, 35636304386103220800, 778379605589616030000

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)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));

Crossrefs

Cf. A052830, A375556, A375558.

Cf. A351155.

Sequence in context: A013494 A375586 A375557 * A365972 A290580 A038122

Adjacent sequences: A375164 A375165 A375166 * A375168 A375169 A375170

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2024

Status

approved