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

2,2

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

Sequence in context: A269675 A269406 A269603 * A075848 A096979 A269464

Adjacent sequences: A027907 A027908 A027909 * A027911 A027912 A027913

Keyword

nonn

Author

Clark Kimberling

Status

approved