%I #7 Mar 07 2024 01:30:40
%S 1,0,2,6,84,860,14430,257082,5678456,140241096,3952791450,
%T 123539438990,4266378769092,160943793753756,6592371152535350,
%U 291260465060881890,13809548247503299440,699362685890810753552,37679514498664685654706
%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*exp(x)) ).
%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)} k^(n-2*k) * (n+k)!/(k! * (n-2*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*exp(x)))/x))
%o (PARI) a(n) = sum(k=0, n\2, k^(n-2*k)*(n+k)!/(k!*(n-2*k)!))/(n+1);
%Y Cf. A213644, A370985.
%Y Cf. A358080, A370927.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 06 2024