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

%I #14 Mar 30 2024 02:37:51

%S 1,2,15,126,1211,12544,136668,1543696,17914325,212308682,2558783193,

%T 31265632206,386430721728,4822586987324,60686262591525,

%U 769167948066520,9810280980482827,125819903217235130,1621648696092783746,20993171222948561746,272848383910348808089

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

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

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

%Y Cf. A371578, A371585.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024