A375237 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^2.

1, 0, 0, 6, 0, 30, 540, 420, 15120, 192780, 623700, 15467760, 187110000, 1394593200, 30353483160, 401350950000, 4974611241600, 105201040744800, 1624218256861200, 27525899782180800, 599214125325816000, 10967831645346576000, 227431647445400798400

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A375167, A375682.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2/2))^2))

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375167.

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(k,n-2*k)|/(2^k*k!).