A356967 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2/2 * A(x)).

1, 0, 0, 3, 6, 20, 540, 4284, 35700, 698760, 10591560, 155024100, 3231336240, 68704908480, 1451024062488, 35843008924800, 950925111973200, 25881184257364800, 765471782499860160, 24210772652940214320, 797021694060934204800, 27752674398657594805440

Offset: 0

Author

Seiichi Manyama, Sep 06 2022

Keywords

• nonn

Crossrefs

Cf. A184949, A349556, A356968.

Cf. A356752, A356962.

Programs

PARI

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

Formula

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