A366496 - OEIS

%I #10 Oct 11 2023 08:40:15

%S 1,1,6,36,251,1891,15007,123593,1046444,9052330,79660406,710879890,

%T 6418000050,58515227946,538008396198,4982752630656,46442071874398,

%U 435299781856712,4100411743983559,38797120485576155,368561495153257186,3513923237883474314

%N G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(5/2)*A(x)^(7/2).

%F G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366435.

%F a(n) = Sum_{k=0..n} binomial(5*k/2,n-k) * binomial(7*k/2,k) / (5*k/2+1).

%o (PARI) a(n) = sum(k=0, n, binomial(5*k/2, n-k)*binomial(7*k/2, k)/(5*k/2+1));

%Y Cf. A001006, A366221, A366272, A366273, A366495, A366497, A366498, A366499, A366500, A366501.

%Y Cf. A366435.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 11 2023