A067294 Third column of triangle A028364.

5, 9, 23, 66, 202, 645, 2123, 7150, 24518, 85306, 300390, 1068484, 3833364, 13855085, 50401395, 184392150, 677998830, 2504191470, 9286661010, 34564913820, 129077071500, 483474711330, 1815928888254

Offset: 0

Author

Wolfdieter Lang, Feb 05 2002

Keywords

• nonn
• easy

Comments

The first two columns give: A000108 (Catalan) and A005807. The next two columns give: A067295-6.

Crossrefs

First differences are in A071747.

Formula

a(n)= A028364(n+2, 2) = C(0)*C(n+2)+C(1)*C(n+1)+C(2)*C(n), with the Catalan numbers C(n)=A000108(n). a(n)= ((11*n^2+28*n+15)/(2*(2*n+1)*(2*n+3)))*C(n+2).

G.f.: (c2(x)*c(x)-(c2(x)-1)/x)/x^2, with c2(x) := 1+x+2*x^2 and c(x) G.f. for Catalan numbers A000108.