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 A381753 #14 Mar 07 2025 10:47:16
%S A381753 1,4,50,846,16495,349240,7803823,181135830,4324897697,105543188190,
%T A381753 2620784850325,66005699547352,1682046970846570,43291586055360034,
%U A381753 1123707191010320955,29382536610737191930,773229801368332554273,20463493681189771623960
%N A381753 Expansion of exp( Sum_{k>=1} binomial(5*k-1,2*k-1) * x^k/k ).
%F A381753 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(5*k-1,2*k-1) * a(n-k).
%F A381753 G.f.: B(x)^2, where B(x) is the g.f. of A060941.
%F A381753 a(n) = 2 * Sum_{k=0..n} binomial(5*n+2*k+2,k) * binomial(5*n+2,n-k)/(5*n+2*k+2).
%o A381753 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(5*k-1, 2*k-1)*x^k/k)))
%o A381753 (PARI) a(n) = 2*sum(k=0, n, binomial(5*n+2*k+2, k)*binomial(5*n+2, n-k)/(5*n+2*k+2));
%Y A381753 Cf. A006013, A079489, A182960, A381751, A381752, A381757, A381758.
%Y A381753 Cf. A060941.
%K A381753 nonn,easy
%O A381753 0,2
%A A381753 _Seiichi Manyama_, Mar 06 2025