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 A381867 #10 Mar 09 2025 09:55:33
%S A381867 1,3,10,44,239,1464,9610,65946,466951,3385259,24999475,187385168,
%T A381867 1421901090,10901237530,84312106160,657031204068,5153954345309,
%U A381867 40663760712441,322478148002872,2569086552458460,20551321340065924,165009872444132477,1329352163579556971,10742386009423170696
%N A381867 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108.
%F A381867 a(n) = Sum_{k=0..n} binomial(3*k+1,k) * binomial(n+k+1,n-k)/(3*k+1).
%F A381867 a(n) = (1 + n)*hypergeom([1/3, 2/3, -n, 2+n], [1, 3/2, 3/2], -3^3/2^4). - _Stefano Spezia_, Mar 09 2025
%o A381867 (PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(n+k+1, n-k)/(3*k+1));
%Y A381867 Cf. A188687, A366034.
%Y A381867 Cf. A000108.
%K A381867 nonn
%O A381867 0,2
%A A381867 _Seiichi Manyama_, Mar 08 2025