A371227 E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^2).

1, 0, 2, 3, 56, 390, 6384, 92400, 1812768, 38565072, 949927680, 25934040000, 783458550720, 25909868761920, 930720395219328, 36108805836317760, 1504050682102456320, 66964478742976711680, 3173178938051223889920, 159461567895099436047360

Offset: 0

Author

Seiichi Manyama, Mar 15 2024

Keywords

• nonn

Crossrefs

Cf. A371228, A371229, A371230.

Cf. A371117.

Programs

PARI

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

Formula

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