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%I #13 Mar 07 2024 01:31:29
%S 1,0,2,3,76,425,10326,119077,3158968,57929265,1740086290,44066266541,
%T 1512768107940,48660920528233,1905202422005806,73878129769929045,
%U 3275941116578461936,147981592692778718561,7366814796135956094378,378666415166758834858237
%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n+k)! * Stirling2(n-k,k)/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1)))/x))
%o (PARI) a(n) = sum(k=0, n\2, (n+k)!*stirling(n-k, k, 2)/(n-k)!)/(n+1);
%Y Cf. A052894, A370989, A370990.
%Y Cf. A370991, A370992.
%Y Cf. A052848.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 06 2024
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