%I #9 Mar 07 2024 01:31:08
%S 1,0,1,3,24,220,2535,35931,588028,11110212,236355885,5605425595,
%T 146586048906,4190560545678,130037568893323,4352949788266275,
%U 156362710268877960,5999465853656510056,244887352806333261753,10595948826118665719475,484448170190529051468910
%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2/2*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)!/(2^k * k! * (n-2*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2/2*exp(x)))/x))
%o (PARI) a(n) = sum(k=0, n\2, k^(n-2*k)*(n+k)!/(2^k*k!*(n-2*k)!))/(n+1);
%Y Cf. A213644, A370987.
%Y Cf. A346888, A370930.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Mar 06 2024
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