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 A381830 #9 Mar 08 2025 09:39:53
%S A381830 1,2,10,69,558,4946,46506,455587,4599494,47517909,499933964,
%T A381830 5337957532,57694565830,630010984557,6939976239376,77027050722166,
%U A381830 860564349616694,9670164031087137,109221767288604000,1239281689627682221,14119315749935075540,161460732437631678114
%N A381830 G.f. A(x) satisfies A(x) = C(x*A(x)^2) / (1 - x*A(x)), where C(x) is the g.f. of A000108.
%F A381830 a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(2*n,n-k)/(n+3*k+1).
%o A381830 (PARI) a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n, n-k)/(n+3*k+1));
%Y A381830 Cf. A364592, A381818, A381831.
%Y A381830 Cf. A000108, A381778.
%K A381830 nonn
%O A381830 0,2
%A A381830 _Seiichi Manyama_, Mar 08 2025