%I #7 Nov 25 2024 09:07:45
%S 1,2,12,74,464,2997,19704,131140,880912,5960000,40555117,277251834,
%T 1902791048,13101878220,90468268336,626202992439,4343671952768,
%U 30186478566432,210131106485088,1464920605002240,10226302297174509,71474029751497258,500097817634501780
%N a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k,n-k).
%F a(n) = [x^n] (1 + x + x * (1 + x)^4)^n.
%o (PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+3*k, n-k));
%Y Cf. A000984, A082759, A378403.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 25 2024