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A027910 T(2n,n-2), T given by A027907. 1
1, 6, 36, 210, 1221, 7098, 41328, 241128, 1409895, 8260934, 48497064, 285219090, 1680166215, 9912297150, 58558256496, 346371955776, 2051126447742, 12158963346852, 72147074769640, 428476010502582, 2546776668682323, 15149061841758174, 90175327717962024 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 11:41 EDT 2021. Contains 348212 sequences. (Running on oeis4.)