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 A382038 #17 Mar 15 2025 09:42:34
%S A382038 1,1,11,244,8285,381096,22175167,1562582848,129381990201,
%T A382038 12313784396800,1324663415429651,158957183013686784,
%U A382038 21051725357219126869,3050121640032545419264,479928476696367747954375,81499293517054315684642816,14856515462975583258374526833,2893604521320117995839047401472
%N A382038 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^4) ), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
%F A382038 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^4).
%F A382038 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(4*n,k)/(n-k-1)! for n > 0.
%F A382038 E.g.f.: exp( Series_Reversion( x*exp(-x)/(1+x)^4 ) ).
%o A382038 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(4*n, k)/(n-k-1)!));
%Y A382038 Cf. A052873, A382036, A382037.
%Y A382038 Cf. A002293, A382034.
%K A382038 nonn
%O A382038 0,3
%A A382038 _Seiichi Manyama_, Mar 12 2025