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 A379085 #10 Dec 15 2024 06:45:38
%S A379085 1,2,6,26,142,802,4434,24222,132686,733076,4081926,22853052,128427106,
%T A379085 723862856,4090573570,23170106086,131515806574,747875338152,
%U A379085 4259810283828,24298797944956,138787172202182,793651842511512,4543393775520936,26035130683198684,149325002408646002
%N A379085 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(2*n+k,n-3*k).
%F A379085 a(n) = [x^n] 1/( 1/(1 + x) - x^3 )^(2*n).
%F A379085 a(n) == 0 (mod 2) for n>0.
%o A379085 (PARI) a(n) = sum(k=0, n\3, binomial(2*n+k-1, k)*binomial(2*n+k, n-3*k));
%Y A379085 Cf. A379022, A379084.
%Y A379085 Cf. A379089.
%K A379085 nonn
%O A379085 0,2
%A A379085 _Seiichi Manyama_, Dec 15 2024