A378152 - OEIS

%I #7 Nov 18 2024 07:33:18

%S 1,0,0,0,1,4,6,4,5,32,112,224,302,488,1564,4872,11034,19664,37128,

%T 95824,266659,635740,1306682,2706524,6503711,16794992,40634744,

%U 90066416,197648134,465436936,1152867388,2790870536,6434526866,14640368240,34415925816,83509570992

%N G.f. A(x) satisfies A(x) = 1 + (x * (1+x) * A(x))^4.

%F a(n) = Sum_{k=0..floor(n/4)} binomial(4*k,n-4*k) * binomial(4*k,k)/(3*k+1).

%o (PARI) a(n) = sum(k=0, n\4, binomial(4*k, n-4*k)*binomial(4*k, k)/(3*k+1));

%Y Cf. A000045, A256169, A378151.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Nov 18 2024