A370462 E.g.f. satisfies A(x) = log(1 + x)/(1 - A(x))^2.

0, 1, 3, 32, 506, 11254, 319486, 11063352, 452075928, 21295486272, 1136180493504, 67720154888352, 4459760039965248, 321592207168637664, 25201588848786782688, 2132592146864957906688, 193806614782424556184320, 18825630812739265968357120

Offset: 0

Author

Seiichi Manyama, Mar 18 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A087138, A370463.

Programs

Mathematica

Table[Sum[(3*k - 2)!/(2*k - 1)!*StirlingS1[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, 1));

Formula

a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * Stirling1(n,k).

a(n) ~ n^(n-1) / (sqrt(2) * (exp(4/27) - 1)^(n - 1/2) * exp(n + 2/27)). - Vaclav Kotesovec, Mar 19 2024

E.g.f.: Series_Reversion( exp(x * (1 - x)^2) - 1 ). - Seiichi Manyama, Sep 09 2024