A067297 Convolution of C(2,2; n) := A064340(n) (generalized Catalan numbers) with itself.

1, 2, 9, 64, 584, 6144, 70576, 859520, 10909440, 142773760, 1913027840, 26115182592, 361936623616, 5079287545856, 72033971859456, 1030768222437376, 14864066521333760, 215791593346695168

Offset: 0

Author

Wolfdieter Lang, Feb 05 2002

Keywords

• nonn
• easy

Crossrefs

Bisections: a(2*k) = A067320(k), a(2*k+1) = 2*A067321(k), k>=0.

Formula

a(n) = Sum_{k=0..n} C(2, 2; k)*C(2, 2; n-k).

G.f.: ((3+c(4*x))/(2*(1-2*x*c(4*x))*(1+c(4*x))))^2, with c(x) g.f. for A000108 (Catalan). Also: (c(4*x)*(3+c(4*x)))^2/(1+c(4*x))^4, or (-1+36*x +(1+24*x)*c(4*x))/((1-4*x)*(1+20*x)*c(4*x)-1+44*x-16*x^2).