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 A381875 #9 Mar 09 2025 09:55:38
%S A381875 1,3,13,66,368,2185,13570,87147,574241,3861286,26390591,182798850,
%T A381875 1280387583,9053335674,64534088960,463249047099,3345832486407,
%U A381875 24296575830677,177286818019264,1299208549351640,9557974679439901,70563100013789595,522608148884843970
%N A381875 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108.
%F A381875 a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(3*n-3*k+1,n-k)/(n+k+1).
%F A381875 a(n) = binomial(1 + 3*n, n)*hypergeom([-1/2-n, -n, 1+n], [-1/3-n, 1/3-n], 2^2/3^3)/(1 + n). - _Stefano Spezia_, Mar 09 2025
%o A381875 (PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(3*n-3*k+1, n-k)/(n+k+1));
%Y A381875 Cf. A129442, A381876, A381877.
%Y A381875 Cf. A000108.
%K A381875 nonn
%O A381875 0,2
%A A381875 _Seiichi Manyama_, Mar 09 2025