A371046 E.g.f. satisfies A(x) = 1 + x^3*A(x)^2*exp(x*A(x)).

1, 0, 0, 6, 24, 60, 1560, 25410, 242256, 3508344, 85882320, 1724406750, 32784999720, 839182482996, 24162605028744, 659439484706730, 19415319297457440, 658935736181053680, 23245444335085544736, 835819877947421773494, 32462532011236141677240

Offset: 0

Author

Seiichi Manyama, Mar 09 2024

Keywords

• nonn

Crossrefs

Cf. A370985, A371019, A371044, A371045.

Cf. A365286.

Programs

PARI

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

Formula

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