A067299 Second column of triangle A067298.

2, 5, 32, 284, 2960, 33872, 411776, 5221568, 68299520, 914858240, 12486496256, 173031701504, 2428066058240, 34432752275456, 492697174507520, 7104716644990976, 103142445617709056, 1506248913346691072

Offset: 0

Author

Wolfdieter Lang, Feb 05 2002

Keywords

• nonn
• easy

Crossrefs

Cf. A064340 (first column), A067300 (third column).

Formula

a(n)=A067298(n+1, 1).

G.f.: ((1+x)*c(2, 2; x)-1)/x, with c(2, 2; x) := (1-3*x*c(4*x))/(1-2*x*c(4*x))^2 g.f. for A064340 and c(x) is g.f. for A000108 (Catalan).

G.f.: (2+x + 12*x*(1+x)*c(4*x))/(1+2*x)^2, where c(x) is g.f. for A000108 (Catalan). - Wolfdieter Lang, May 05 2006.

Conjecture: n*(17*n-7)*a(n) +2*(-119*n^2+270*n-96)*a(n-1) -16*(17*n+10)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jul 21 2016