A377810 E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^2.

1, 3, 17, 154, 1993, 34066, 728209, 18733926, 564117425, 19473863986, 758421401401, 32901791851006, 1573602042306265, 82267318018246986, 4667656830688700801, 285662368622361581206, 18758565855176593500385, 1315663025587514658845026, 98160436697525045768511721

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.: exp( -LambertW(-x/(1-x)^2) )/(1-x)^2.

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

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

a(n) ~ 2^(n + 3/2) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(3/2) * (1 + 2*exp(-1) - sqrt(1 + 4*exp(-1)))^(n + 1/2) * exp(2*n+1)). - Vaclav Kotesovec, Nov 11 2024

Prog

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

Crossrefs

Cf. A352410, A377811.

Cf. A362775, A377742.

Sequence in context: A318987 A353258 A208832 * A135751 A368444 A168441

Adjacent sequences: A377807 A377808 A377809 * A377811 A377813 A377814

Keyword

nonn

Author

Seiichi Manyama, Nov 08 2024

Status

approved