Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #18 Sep 08 2024 13:48:23
%S 0,1,5,56,1022,26054,853426,34150584,1614418536,88035438144,
%T 5439554576064,375580703703072,28658577826251072,2394815612176027104,
%U 217504341217879448352,21333409628052488832768,2247318076016738768083200,253054488675536428638723840
%N E.g.f. satisfies A(x) = -log(1 - x)/(1 - A(x))^2.
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * |Stirling1(n,k)|.
%F a(n) ~ n^(n-1) / (sqrt(2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - _Vaclav Kotesovec_, Mar 19 2024
%F E.g.f.: Series_Reversion( 1 - exp(-x * (1 - x)^2) ). - _Seiichi Manyama_, Sep 08 2024
%p A371314 := proc(n)
%p add((3*k-2)!/(2*k-1)!*abs(stirling1(n,k)),k=1..n) ;
%p end proc:
%p seq(A371314(n),n=0..40) ; # _R. J. Mathar_, Mar 25 2024
%t Table[Sum[(3*k-2)!/(2*k-1)! * Abs[StirlingS1[n, k]], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 19 2024 *)
%o (PARI) a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*abs(stirling(n, k, 1)));
%Y Cf. A052851, A371315.
%Y Cf. A370462.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 18 2024