A366497 - OEIS

%I #9 Oct 11 2023 08:40:11

%S 1,1,8,64,596,6028,64352,713812,8146490,95040886,1128369960,

%T 13588883712,165598378308,2038279921692,25303322898120,

%U 316443054086214,3983011314348183,50418720131975193,641444450506307160,8197477211343267688,105185927879224420064

%N G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(7/2)*A(x)^(9/2).

%F G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366437.

%F a(n) = Sum_{k=0..n} binomial(7*k/2,n-k) * binomial(9*k/2,k) / (7*k/2+1).

%o (PARI) a(n) = sum(k=0, n, binomial(7*k/2, n-k)*binomial(9*k/2, k)/(7*k/2+1));

%Y Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366498, A366499, A366500, A366501.

%Y Cf. A366437.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 11 2023