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 A381783 #9 Mar 07 2025 10:47:24
%S A381783 1,2,11,79,645,5682,52643,505575,4987933,50250625,514787110,
%T A381783 5346336739,56161123273,595667090038,6370314162095,68616488830785,
%U A381783 743733580011957,8106009997644507,88783190884441892,976705067814061730,10787334777299825522,119569153425125828365
%N A381783 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x*A(x)), where C(x) is the g.f. of A000108.
%F A381783 a(n) = (1/(3*n+1)) * Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-2*k+1,n-k).
%o A381783 (PARI) a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-2*k+1, n-k))/(3*n+1);
%Y A381783 Cf. A212071, A381773, A381782.
%Y A381783 Cf. A000108.
%K A381783 nonn
%O A381783 0,2
%A A381783 _Seiichi Manyama_, Mar 07 2025