A371371 E.g.f. satisfies A(x) = exp(x/(1 - A(x))^2) - 1.

0, 1, 5, 61, 1209, 33261, 1171933, 50363293, 2554659761, 149399423101, 9896519640981, 732401926901613, 59890184672573929, 5362586032967290765, 521831581416561627149, 54834132144912233219581, 6188110724712474697469025, 746431260858514472012500701

Offset: 0

Author

Seiichi Manyama, Mar 20 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A368033, A371370.

Cf. A052892.

Programs

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*log(1+x)))))

PARI

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

Formula

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

a(n) = Sum_{k=1..n} (2*n+k-2)!/(2*n-1)! * Stirling2(n,k).

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