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 A380945 #10 Feb 09 2025 09:18:51
%S A380945 1,4,50,1124,37192,1637232,90278176,5992556320,465599728512,
%T A380945 41470892979200,4167168740195584,466428111222196224,
%U A380945 57556315795242096640,7763511917730857967616,1136484206117494859980800,179453678311835212416585728,30404317385796994658988752896
%N A380945 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-2*x) ).
%H A380945 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380945 E.g.f. A(x) satisfies A(x) = exp(2*x*A(x))/(1 - x*A(x))^2.
%F A380945 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380723.
%F A380945 a(n) = 2 * n! * Sum_{k=0..n} (2*n+2)^(k-1) * binomial(3*n-k+1,n-k)/k!.
%o A380945 (PARI) a(n, q=2, r=2, s=2, t=0, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
%Y A380945 Cf. A370054, A377832.
%Y A380945 Cf. A380646, A380723.
%K A380945 nonn
%O A380945 0,2
%A A380945 _Seiichi Manyama_, Feb 09 2025