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 A376443 #12 Sep 23 2024 09:28:39
%S A376443 1,0,0,12,0,120,10800,1680,766080,55913760,48686400,12973625280,
%T A376443 878369184000,2257312337280,475877474392320,31178226637958400,
%U A376443 176135891323392000,32566007822802854400,2111180034178805990400,22027962609483730099200,3749400628293386626560000,244391453278125083388057600
%N A376443 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^2 ).
%H A376443 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376443 E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x) * (exp(x^2*A(x)^2) - 1))^2.
%F A376443 a(n) = (2 * n!/(2n+2)!) * Sum_{k=0..floor(n/2)} (3*n-2*k+1)! * Stirling2(k,n-2*k)/k!.
%o A376443 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^2)/x))
%o A376443 (PARI) a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*stirling(k, n-2*k, 2)/k!)/(2*n+2)!;
%Y A376443 Cf. A376345, A376444.
%Y A376443 Cf. A375664.
%K A376443 nonn
%O A376443 0,4
%A A376443 _Seiichi Manyama_, Sep 22 2024