A366237 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^3*A(x)^2.
1, 2, 7, 33, 161, 843, 4601, 25896, 149254, 876480, 5225616, 31547730, 192470212, 1184804588, 7349888208, 45902094845, 288368474907, 1821096958308, 11554270204142, 73615309821574, 470795634833760, 3021222108762826, 19448517295201332
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, binomial(4*k+1, n-k)*binomial(2*k, k)/(k+1));
Formula
G.f.: 2*(1+x) / (1 + sqrt(1-4*x*(1+x)^4)).
a(n) = Sum_{k=0..n} binomial(4*k+1,n-k) * binomial(2*k,k)/(k+1).