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 A380080 #9 Jan 12 2025 07:56:27
%S A380080 1,1,3,15,109,1045,12501,179599,3015657,57988809,1257058585,
%T A380080 30337358491,806837271021,23448335293981,739379851041573,
%U A380080 25143044445680295,917252832237053521,35735484803144976145,1480838869407287923569,65038486139094829172275,3017945328547452509505045
%N A380080 Expansion of e.g.f. (1/x) * Series_Reversion( x / sqrt(1 + 2*x*exp(x)) ).
%F A380080 E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*A(x)*exp(x*A(x)) ).
%F A380080 a(n) = (n!/(n+1)) * Sum_{k=0..n} 2^k * k^(n-k) * binomial(n/2+1/2,k)/(n-k)!.
%o A380080 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n/2+1/2, k)/(n-k)!)/(n+1);
%Y A380080 Cf. A161633, A380081.
%Y A380080 Cf. A380050.
%K A380080 nonn
%O A380080 0,3
%A A380080 _Seiichi Manyama_, Jan 11 2025