A027910 T(2n,n-2), T given by A027907.

1, 6, 36, 210, 1221, 7098, 41328, 241128, 1409895, 8260934, 48497064, 285219090, 1680166215, 9912297150, 58558256496, 346371955776, 2051126447742, 12158963346852, 72147074769640, 428476010502582, 2546776668682323, 15149061841758174, 90175327717962024

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

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

Programs

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

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