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 A381780 #9 Mar 07 2025 10:47:35
%S A381780 1,2,13,122,1348,16317,209366,2797461,38509302,542367569,7778173646,
%T A381780 113196865436,1667497600735,24816081138489,372551391235504,
%U A381780 5635157636123317,85797446797707896,1313857342649814042,20222887980813290849,312694810135597988049,4854881337618505385339
%N A381780 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * C(x*A(x)^3), where C(x) is the g.f. of A000108.
%F A381780 a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(2*n+k+1,n-k)/(2*n+3*k+1).
%o A381780 (PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(2*n+k+1, n-k)/(2*n+3*k+1));
%Y A381780 Cf. A007852, A069271, A381772.
%Y A381780 Cf. A000108.
%K A381780 nonn
%O A381780 0,2
%A A381780 _Seiichi Manyama_, Mar 07 2025