A365054 E.g.f. satisfies A(x) = exp( x * (1+x/2) * A(x)^2 ).

1, 1, 6, 64, 1038, 22666, 624448, 20801628, 813473468, 36543076444, 1854702411336, 104970490358944, 6555275229438664, 447773277245296536, 33211911279540910400, 2658266282912883209296, 228375288313274403201552, 20961681963345040127314192

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..348

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

Formula

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

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

From Vaclav Kotesovec, Nov 10 2023: (Start)

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

a(n) ~ sqrt((-sqrt(1 + exp(-1)) + 1 + exp(-1))/2) * n^(n-1) / (exp(n-1) * (-1 + sqrt(1 + exp(-1)))^n). (End)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x/2))/2)))

Crossrefs

Cf. A365053, A365055, A365056.

Cf. A362474, A362773.

Sequence in context: A354494 A370894 A258425 * A249592 A333983 A087488

Adjacent sequences: A365051 A365052 A365053 * A365055 A365056 A365057

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2023

Status

approved