A371316 E.g.f. satisfies A(x) = (exp(x) - 1)/(1 - A(x))^2.

0, 1, 5, 55, 1001, 25471, 832265, 33209695, 1565233241, 85089724831, 5241027586025, 360724089079135, 27436914192242681, 2285358551395272991, 206893372546088226185, 20226992715373747441375, 2123855112711652849031321, 238375283773978224211297951

Offset: 0

Author

Seiichi Manyama, Mar 18 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052886, A371317.

Programs

Mathematica

Table[Sum[(3*k-2)!/(2*k-1)! * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)

PARI

a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*stirling(n, k, 2));

Formula

a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * Stirling2(n,k).

a(n) ~ sqrt(31) * n^(n-1) / (sqrt(2) * 3^(3/2) * log(31/27)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Mar 19 2024

E.g.f.: Series_Reversion( log(1 + x * (1 - x)^2) ). - Seiichi Manyama, Sep 08 2024