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

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n)=sum(C(2, 2; k)C(2, 2; n-k), k=0..n).

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).

Crossrefs

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

Sequence in context: A289717 A094100 A185897 * A274394 A368291 A113882

Adjacent sequences: A067294 A067295 A067296 * A067298 A067299 A067300

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 05 2002

Status

approved