This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371020 #10 Mar 08 2024 08:00:27
%S A371020 1,0,1,3,18,160,1545,19131,273868,4463460,82561545,1695986875,
%T A371020 38413504866,951203750718,25551218851249,740338919242755,
%U A371020 23014265170565880,764047265130952456,26981593786255568913,1009915667787285212787,39938889756657408019390
%N A371020 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^2/2*exp(x)) ).
%H A371020 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371020 a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(n+1,k)/(2^k * (n-2*k)!).
%o A371020 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^2/2*exp(x)))/x))
%o A371020 (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n+1, k)/(2^k*(n-2*k)!))/(n+1);
%Y A371020 Cf. A370889.
%K A371020 nonn
%O A371020 0,4
%A A371020 _Seiichi Manyama_, Mar 08 2024