A067295 Fourth column of triangle A028364.

14, 28, 76, 227, 715, 2333, 7810, 26663, 92456, 324700, 1152464, 4127294, 14895145, 54115895, 197764350, 726473055, 2680979820, 9934884960, 36953107320, 137913387450, 516295313430, 1938260223354

Offset: 0

Author

Wolfdieter Lang, Feb 05 2002

Keywords

• nonn
• easy

Crossrefs

Cf. A067294 (third column), A067296 (fifth column).

Formula

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

a(n)= (3*(31*n^3+163*n^2+254*n+112)/(8*(2*n+1)*(2*n+3)*(2*n+5)))*C(n+3).

G.f.: (c3(x)*c(x)-(c3(x)-1)/x)/x^3, with c3(x) := 1+x+2*x^2+5*x^3 and c(x) G.f. for Catalan numbers A000108.