A366182 - OEIS

%I #9 Oct 03 2023 09:00:08

%S 1,4,19,128,1037,9221,86847,851073,8586951,88598014,930473246,

%T 9913648325,106891041270,1164153791878,12788021717902,141518588447588,

%U 1576271179332762,17657110535606919,198792746866201879,2248222906227731856,25529220583699163958

%N G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x).

%F a(n) = Sum_{k=0..n} binomial(n+6*k+2,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+6*k+2, n-k)*binomial(3*k, k)/(2*k+1));

%Y Partial sums of A366180.

%Y Cf. A364623, A366183, A366184.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 03 2023