A371586 - OEIS

%I #14 Mar 29 2024 15:21:43

%S 1,2,13,106,986,9898,104535,1144630,12876908,147937396,1728352171,

%T 20471245898,245254954252,2966792716710,36186910210761,

%U 444559817944096,5495828249436652,68318636646858588,853455362282694440,10708603125245767280,134897492549870974674

%N G.f. satisfies A(x) = ( 1 + x*A(x)^2 * (1 + x*A(x)^2)^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(s*k,n-k)/(t*k+u*(n-k)+r).

%o (PARI) a(n, r=2, s=2, t=4, u=4) = 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. A367282.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024