A376146 E.g.f. satisfies A(x) = exp( x * (1+x)^4 * A(x) ).

1, 1, 11, 124, 1997, 42616, 1120327, 35203960, 1288741337, 53898829408, 2536932089771, 132770439164584, 7649993702503429, 481295935534882768, 32834728249861856879, 2414570451161244199576, 190412665638185073399473, 16030575396743899522805440

Offset: 0

Author

Seiichi Manyama, Sep 11 2024

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362771, A362772, A376145.

Cf. A360082, A367790.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)^4))))

Formula

E.g.f.: exp( -LambertW(-x * (1+x)^4) ).

a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(4*k,n-k)/k!.