A362776 E.g.f. satisfies A(x) = exp( x/(1-x)^2 * A(x)^2 ).

1, 1, 9, 127, 2601, 70981, 2433673, 100697787, 4886085137, 272168650441, 17121437245161, 1200717094233559, 92892754255837561, 7859587210132504653, 721996671783802854377, 71564871858940414914451, 7613407794191946986893857, 865285095267929315207801233

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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} (2*k+1)^(k-1) * binomial(n+k-1,n-k)/k!.

From Vaclav Kotesovec, Nov 10 2023: (Start)

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

a(n) ~ sqrt(-sqrt(1 + 2*exp(-1)) + 1 + 2*exp(-1)) * n^(n-1) / (sqrt(2) * (-1 + sqrt(1 + 2*exp(-1)))^(3/2) * (-sqrt(1 + 2*exp(-1)) + 1 + exp(-1))^(n - 1/2) * exp(2*n - 1/2)). (End)

Prog

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

Crossrefs

Cf. A082579, A362775.

Cf. A361065.

Sequence in context: A092651 A366036 A258294 * A365033 A073014 A046754

Adjacent sequences: A362773 A362774 A362775 * A362777 A362778 A362779

Keyword

nonn

Author

Seiichi Manyama, May 02 2023

Status

approved