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 A380035 #23 Jan 11 2025 10:27:53
%S A380035 1,1,5,42,517,8420,171201,4181128,119339081,3900501648,143703797725,
%T A380035 5893732487456,266358266633229,13153210420876864,704697559381904921,
%U A380035 40714369264722337920,2523456287242464370321,167019778198736205721856,11757749450929277192860725
%N A380035 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)) ).
%F A380035 a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(n/2+k/2+1/2,k)/( (n+k+1)*(n-k)! ).
%o A380035 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n/2+k/2+1/2, k)/((n+k+1)*(n-k)!));
%Y A380035 Cf. A380015, A380042.
%K A380035 nonn
%O A380035 0,3
%A A380035 _Seiichi Manyama_, Jan 10 2025