A368033 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))^2).

0, 1, 3, 26, 370, 7334, 186468, 5787144, 212100208, 8964974016, 429304991880, 22971063265776, 1358260804832160, 87949592273821680, 6189420503357272608, 470384337802047909120, 38393707193347187344896, 3349704214386311986028160

Offset

0,3

Links

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

Index entries for reversions of series

Formula

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

a(n) = Sum_{k=1..n} (2*n+k-2)!/(2*n-1)! * Stirling1(n,k).

a(n) ~ LambertW(2*exp(1))^n * n^(n-1) / (sqrt(2*(1 + LambertW(2*exp(1)))) * exp(n) * (2 - LambertW(2*exp(1)))^(3*n - 1)). - Vaclav Kotesovec, Mar 29 2024

Prog

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

Crossrefs

Cf. A371370, A371371.

Cf. A371342.

Sequence in context: A206404 A373425 A262301 * A376067 A317654 A143155

Adjacent sequences: A368030 A368031 A368032 * A368034 A368035 A368036

Keyword

nonn

Author

Seiichi Manyama, Mar 20 2024

Status

approved