A366437 - OEIS

%I #10 Oct 10 2023 05:08:39

%S 1,1,-7,49,-427,4165,-43435,473977,-5344333,61772179,-727993301,

%T 8714701219,-105672771225,1295237037815,-16021641194545,

%U 199747074505773,-2507395464414008,31664298046926328,-401994771266030880,5127701624204157600,-65684716411944207144

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

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

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

%Y Partial sums give A366406.

%Y Cf. A366431, A366432, A366433, A366434, A366435, A366436.

%K sign

%O 0,3

%A _Seiichi Manyama_, Oct 09 2023