A378019 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x) ).

1, 2, 9, 79, 957, 15441, 309943, 7468301, 210221385, 6774449185, 246049105131, 9947338595085, 443121311695021, 21568178966624993, 1138938283455953919, 64856665518838006861, 3961941908569940501649, 258453847468153873181889, 17932482767578645884498643

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Formula

E.g.f.: (1+x) * exp( -LambertW(-x * (1+x)^2) ).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)*exp(-lambertw(-x*(1+x)^2))))
(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(2*k+1, n-k)/k!);

Crossrefs

Cf. A362772, A377827.

Cf. A377963.

Sequence in context: A229211 A056918 A346671 * A194471 A369712 A215629

Adjacent sequences: A378016 A378017 A378018 * A378020 A378021 A378022

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2024

Status

approved