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 A382036 #20 Mar 15 2025 09:42:05
%S A382036 1,1,7,94,1901,51696,1771267,73317616,3560476761,198531343360,
%T A382036 12502959204671,877829600807424,67991178144166213,5759309535250776064,
%U A382036 529665762441463234875,52560256640090731902976,5597859153748148214250673,636915477940535101583130624,77102760978489789146276986231
%N A382036 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * C(x)^2) ), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A382036 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * C(x*A(x))^2).
%F A382036 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(2*n,k)/(n-k-1)! for n > 0.
%F A382036 E.g.f.: exp( Series_Reversion( x*exp(-x)/(1+x)^2 ) ).
%F A382036 a(n) ~ 2^(n - 1/2) * n^(n-1) / ((sqrt(2) - 1)^(n - 1/2) * exp((sqrt(2) - 1)*(sqrt(2)*n - 1))). - _Vaclav Kotesovec_, Mar 15 2025
%o A382036 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(2*n, k)/(n-k-1)!));
%Y A382036 Cf. A052873, A382037, A382038.
%Y A382036 Cf. A000108, A377829, A382032.
%K A382036 nonn
%O A382036 0,3
%A A382036 _Seiichi Manyama_, Mar 12 2025