A366179 - OEIS

%I #9 Oct 03 2023 08:59:57

%S 1,3,13,80,582,4627,38906,340138,3060404,28151835,263546436,

%T 2502686416,24048985907,233410500126,2284790496700,22530585455108,

%U 223610524426654,2231886642819974,22389017726854323,225604735477075272,2282518274913713101

%N G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x).

%F a(n) = Sum_{k=0..n} binomial(n+4*k+1,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, n-k)*binomial(3*k, k)/(2*k+1));

%Y Partial sums of A366178.

%Y Cf. A364620, A364629, A366180.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 03 2023