A379086 - OEIS

%I #10 Dec 15 2024 06:45:11

%S 1,3,21,174,1509,13443,121962,1120899,10401021,97230090,914283621,

%T 8638552464,81945757734,779949538176,7444735446813,71237074583589,

%U 683125330952205,6563268117869076,63164380112090814,608805362150884731,5875874727915635409,56780302474503539427,549294315060885105744

%N a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n+k,n-2*k).

%F a(n) = [x^n] 1/( 1/(1 + x) - x^2 )^(3*n).

%F a(n) == 0 (mod 3) for n>0.

%o (PARI) a(n) = sum(k=0, n\2, binomial(3*n+k-1, k)*binomial(3*n+k, n-2*k));

%Y Cf. A379025, A379087.

%Y Cf. A379088.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 15 2024