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

0,1

Links

Table of n, a(n) for n=0..21.

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.

Crossrefs

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

Sequence in context: A321371 A077265 A033847 * A212890 A019552 A325728

Adjacent sequences: A067292 A067293 A067294 * A067296 A067297 A067298

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 05 2002

Status

approved