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 A380044 #9 Jan 11 2025 10:27:04
%S A380044 1,1,7,81,1393,32025,924831,32208337,1314511297,61553580849,
%T A380044 3253663709335,191661481308561,12451241630689137,884434637282286025,
%U A380044 68195094329460133231,5672843158404577658385,506413381554227338302721,48290505275596520116029537,4899034372132659112326787239
%N A380044 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x)*A(x) ).
%F A380044 a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(3*k/2+1/2,k)/( (3*k+1)*(n-k)! ).
%o A380044 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(3*k/2+1/2, k)/((3*k+1)*(n-k)!));
%Y A380044 Cf. A295238, A380045.
%K A380044 nonn
%O A380044 0,3
%A A380044 _Seiichi Manyama_, Jan 10 2025