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 A371584 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x))^2 )^2. 0

%I #18 Mar 29 2024 15:21:22

%S 1,2,15,138,1435,16074,189238,2308640,28927579,370084760,4814147248,

%T 63482437724,846678807008,11401357736202,154800183842738,

%U 2116833422071448,29128279396373599,403029526567463278,5603854904038673961,78260199678455985082,1097257906416031628336

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

%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

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

%Y Cf. A371579.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024

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Last modified June 25 15:24 EDT 2024. Contains 373705 sequences. (Running on oeis4.)