OFFSET
2,2
COMMENTS
a(n) is also the number of lattice paths from (0,0) to (2n-1,n-2) taking north and east steps avoiding north^{>=3}. - Shanzhen Gao, Apr 20 2010
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..500
FORMULA
a(n) = Sum_{i=0..floor((2*n-3)/2)} C(2*n,n-2-i)*C(n-2-i,i). Shanzhen Gao, Apr 20 2010
G.f.: -g^2*(g^2+g+1)/(3*g^2+g-1) where g = x times the g.f. of A143927. - Mark van Hoeij, Nov 16 2011
a(n) ~ sqrt((221-29*sqrt(13))/78) * ((70+26*sqrt(13))/27)^n/(9*sqrt(Pi*n)). - Vaclav Kotesovec, Aug 25 2014
MAPLE
a:= proc(n) option remember; `if`(n<3, n*(n-1)/2,
(14*(2*n-1)*(65*n^3-120*n^2+37*n+6) *a(n-1)
+36*(n-1)*(2*n-1)*(2*n-3)*(13*n+2) *a(n-2))/
(3*(13*n-11)*(n-2)*(3*n+2)*(3*n+1)))
end:
seq(a(n), n=2..25); # Alois P. Heinz, Aug 07 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved