A371044 E.g.f. satisfies A(x) = 1 + x^3*exp(x*A(x)).

1, 0, 0, 6, 24, 60, 120, 5250, 80976, 726264, 4839120, 86487390, 2283242280, 42585905076, 590667519624, 10115535833130, 286758920451360, 8128299117822960, 186279550983756576, 4123388294626654134, 118916807955913504440, 4102548791571529697580

Offset: 0

Author

Seiichi Manyama, Mar 09 2024

Keywords

• nonn

Crossrefs

Cf. A370985, A371019, A371045, A371046.

Cf. A161631, A371042.

Programs

Mathematica

nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^4]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)

PARI

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

Formula

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