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 A381785 #8 Mar 07 2025 10:47:49
%S A381785 1,2,7,45,335,2731,23573,211741,1958571,18529392,178459000,1743868792,
%T A381785 17246702932,172302244669,1736302280083,17627794322287,
%U A381785 180133941044517,1851310247393202,19123511540724822,198437973436950204,2067524004169000212,21620908821378509071
%N A381785 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^2), where C(x) is the g.f. of A000108.
%F A381785 a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(2*k+1,n-k)/(4*k+1).
%o A381785 (PARI) a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(2*k+1, n-k)/(4*k+1));
%Y A381785 Cf. A212071, A381772, A381778, A381784.
%Y A381785 Cf. A000108.
%K A381785 nonn
%O A381785 0,2
%A A381785 _Seiichi Manyama_, Mar 07 2025