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 A379089 #8 Dec 15 2024 07:25:37
%S A379089 1,1,2,6,24,108,503,2385,11537,56992,286769,1464317,7564803,39457205,
%T A379089 207500615,1099066181,5858206629,31399478619,169132215962,
%U A379089 915057263082,4970445985138,27095859218337,148193424618950,812923791698402,4471543767583949,24657936277287687
%N A379089 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * (1 + x^3*A(x)^7).
%F A379089 G.f. A(x) satisfies A(x) = exp( 1/2 * Sum_{k>=1} A379085(k) * x^k/k ).
%F A379089 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n+k+1,n-3*k)/(2*n+k+1) = (1/(2*n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k,k) * binomial(2*n+k+1,n-3*k).
%o A379089 (PARI) a(n) = sum(k=0, n\3, binomial(2*n+k+1, k)*binomial(2*n+k+1, n-3*k)/(2*n+k+1));
%Y A379089 Cf. A379085.
%K A379089 nonn
%O A379089 0,3
%A A379089 _Seiichi Manyama_, Dec 15 2024