A357088 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2 / 2.

1, 0, 1, 3, 16, 135, 1246, 14238, 192613, 2948025, 51071236, 985911003, 20952667660, 486857940660, 12275673296251, 333786662478363, 9737819506544272, 303399477464036175, 10054949172135522106, 353197317869395005258, 13108298181041284002769

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n-k+1)^(k-1) * Stirling2(n,2*k)/(2^k * k!).

Prog

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

Crossrefs

Cf. A349588, A357089.

Sequence in context: A129043 A182951 A247770 * A277673 A335356 A135746

Adjacent sequences: A357085 A357086 A357087 * A357089 A357090 A357091

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2022

Status

approved