%I #17 Sep 19 2024 14:43:06

%S 1,0,2,3,52,305,4866,57337,1048776,18547713,407900710,9436057961,

%T 248501026236,7021087254337,217488458525898,7223642070331065,

%U 258233053457437456,9841074705853124609,399304906991091898830,17163110041947804495817,779646387683354742170820

%N E.g.f. satisfies A(x) = 1 + x*A(x)*(exp(x*A(x)) - 1).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (n-k+1)! ).

%F E.g.f.: (1/x) * Series_Reversion( x/(1 + x*(exp(x) - 1)) ). - _Seiichi Manyama_, Sep 19 2024

%o (PARI) a(n) = n!^2*sum(k=0, n\2, stirling(n-k, k, 2)/((n-k)!*(n-k+1)!));

%Y Cf. A370988, A371115, A371120.

%Y Cf. A000272, A371139, A376293.

%Y Cf. A371121.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 11 2024