A371233 E.g.f. satisfies A(x) = 1 - x^2*log(1 - x*A(x)^2).

1, 0, 0, 6, 12, 40, 1620, 16128, 154560, 3378240, 67828320, 1247843520, 28996704000, 773215822080, 20900234234880, 609432997219200, 19677823129036800, 674330219708221440, 24327437969162280960, 936555233579552563200, 38250260222888409292800

Offset: 0

Author

Seiichi Manyama, Mar 15 2024

Keywords

• nonn

Crossrefs

Cf. A371234, A371235.

Cf. A371118.

Programs

PARI

a(n) = n!*sum(k=0, n\3, (2*n-4*k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(2*n-5*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (2*n-4*k)! * |Stirling1(n-2*k,k)|/( (n-2*k)! * (2*n-5*k+1)! ).