A356962 E.g.f. satisfies log(A(x)) = x^2/2 * (exp(x*A(x)) - 1) * A(x).

1, 0, 0, 3, 6, 10, 465, 3801, 20608, 461196, 7609185, 85446955, 1661943756, 38070386718, 692342989429, 15023805426735, 404978989779120, 10131679290423736, 264474729910772433, 8059571860456028835, 249785940327179846500, 7837578968934515202570

Offset: 0

Author

Seiichi Manyama, Sep 06 2022

Keywords

• nonn

Crossrefs

Cf. A349557, A356785, A356963.

Cf. A356951, A356967.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * Stirling2(n-2*k,k)/(2^k * (n-2*k)!).