A375682 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^3.

1, 0, 0, 9, 0, 45, 1080, 630, 30240, 470610, 1247400, 38170440, 523908000, 3454050600, 87950182320, 1245647403000, 14580569203200, 346019491818000, 5524280291930400, 92520760776444000, 2188180621979352000, 40781057935225608000, 857154570994798876800

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375167.

a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * |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))^3))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(k, n-2*k, 1))/(2^k*k!))/2;

Crossrefs

Cf. A375167, A375237.

Sequence in context: A182213 A340954 A087094 * A343575 A270010 A167319

Adjacent sequences: A375679 A375680 A375681 * A375683 A375684 A375685

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2024

Status

approved