A362656 E.g.f. satisfies A(x) = exp( x * exp(x) * A(x)^3 ).

1, 1, 9, 145, 3569, 119041, 5025145, 256991953, 15448193633, 1067634195841, 83414064659561, 7270683884044945, 699503964027087697, 73631519384051331457, 8417768844410686595801, 1038658083084399115865041, 137579671405398060549801665

Offset: 0

Author

Seiichi Manyama, Apr 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A273954, A360473, A362671, A362672.

Cf. A052752.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x*exp(x))/3)))

Formula

E.g.f.: exp( -LambertW(-3*x * exp(x))/3 ).

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