A377373 Expansion of e.g.f. (1/x) * Series_Reversion( x / (exp(-x) + 2*x) ).

1, 1, 3, 14, 93, 794, 8335, 103774, 1496313, 24525458, 450478131, 9166307798, 204692557333, 4977320639290, 130918278855351, 3703846153114574, 112155490349101041, 3619411771703973410, 124011196515200953819, 4496024219722304736070, 171963129575721708667341

Offset: 0

Author

Seiichi Manyama, Dec 28 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A108919, A377374.

Cf. A376106.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x/(1-2*x))/x))

PARI

a(n) = n!*sum(k=0, n, (-1)^k*2^(n-k)*(k+1)^(k-1)*binomial(n, k)/k!);

Formula

E.g.f.: (1/x) * LambertW(x / (1 - 2*x)).

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

a(n) = A376106(n+1)/(n+1).