A378612 - OEIS

%I #8 Dec 02 2024 10:09:41

%S 1,3,27,264,2703,28443,304740,3306852,36225519,399755001,4437142467,

%T 49485052224,554059164036,6224177431332,70120015345512,

%U 791898021185484,8962485528377583,101626868754849381,1154295872365035537,13130360954151723480,149562006735075309783

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

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

%F a(n) = (1/4)^n * [x^(3*n)] 3/(1 - x/(1 - x))^n for n > 0.

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

%Y Cf. A002002, A378611, A378613.

%Y Cf. A369012.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 01 2024