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 A380077 #10 Jan 12 2025 07:56:04
%S A380077 1,1,7,87,1621,40485,1271841,48220207,2143450009,109350344745,
%T A380077 6298638659245,404371344546411,28633701543626037,2217105596852342989,
%U A380077 186362307297569836993,16901012222196104542695,1644911203243501609414321,171017059743998995011125457,18916512667390427993433246357
%N A380077 Expansion of e.g.f. (1/x) * Series_Reversion( x * sqrt(1 - 2*x*exp(x)) ).
%F A380077 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*A(x)*exp(x*A(x)) ).
%F A380077 a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(n/2+k+1/2,k)/( (n+2*k+1)*(n-k)! ).
%F A380077 a(n) = (n!/(n+1)) * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(-n/2-1/2,k)/(n-k)!.
%o A380077 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*sqrt(1-2*x*exp(x)))/x))
%o A380077 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n/2+k+1/2, k)/((n+2*k+1)*(n-k)!));
%Y A380077 Cf. A213644, A380078.
%Y A380077 Cf. A380035.
%K A380077 nonn
%O A380077 0,3
%A A380077 _Seiichi Manyama_, Jan 11 2025