|
| |
|
|
A089627
|
|
Triangle T(n,k), 0<=k<=n, read by rows, defined by T(n,k)=C(n,2*k)*C(2*k,k).
|
|
4
| |
|
|
1, 1, 0, 1, 2, 0, 1, 6, 0, 0, 1, 12, 6, 0, 0, 1, 20, 30, 0, 0, 0, 1, 30, 90, 20, 0, 0, 0, 1, 42, 210, 140, 0, 0, 0, 0, 1, 56, 420, 560, 70, 0, 0, 0, 0, 1, 72, 756, 1680, 630, 0, 0, 0, 0, 0, 1, 90, 1260, 4200, 3150, 252, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Row sums : A002426.
The rows of this triangle are the gamma vectors of the n-dimensional type B associahedra (Postnikov et al., p.38 ). Cf. A055151 and A101280. [Peter Bala, Oct 28 2008]
|
|
|
LINKS
| A. Postnikov, V. Reiner, L. Williams, Faces of generalized permutohedra [From Peter Bala, Oct 28 2008]
|
|
|
FORMULA
| T(n, k) = n!/((n-2*k)!*k!*k!).
E.g.f.: exp(x)*BesselI(0, 2*x*sqrt(y)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2005
|
|
|
EXAMPLE
| Triangle begins:
1
1, 0
1, 2, 0
1, 6, 0, 0
1, 12, 6, 0, 0
1, 20, 30, 0, 0, 0
1, 30, 90, 20, 0, 0, 0
1, 42, 210, 140, 0, 0, 0, 0
1, 56, 420, 560, 70, 0, 0, 0, 0
1, 72, 756, 1680, 630, 0, 0, 0, 0, 0
1, 90, 1260, 4200, 3150, 252, 0, 0, 0, 0, 0
1, 110, 1980, 9240, 11550, 2772, 0, 0, 0, 0, 0, 0
1, 132, 2970, 18480, 34650, 16632, 924, 0, 0, 0, 0, 0, 0
Relocating the zeros to be evenly distributed and interpreting the triangle as the coefficients of polynomials
1
1
1 + 2 q^2
1 + 6 q^2
1 + 12 q^2 + 6 q^4
1 + 20 q^2 + 30 q^4
1 + 30 q^2 + 90 q^4 + 20 q^6
1 + 42 q^2 + 210 q^4 + 140 q^6
1 + 56 q^2 + 420 q^4 + 560 q^6 + 70 q^8
then the substitution q^k -> 1/(floor(k/2)+1) gives the Motzkin numbers A001006.
[Peter Luschny, Aug 29 2011]
|
|
|
MAPLE
| for i from 0 to 12 do seq( binomial(i, j)*binomial(i-j, j), j=0..i ); od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2006
|
|
|
CROSSREFS
| Cf. A002426, A055151, A101280.
Sequence in context: A094456 A010028 A151860 * A055925 A161121 A021500
Adjacent sequences: A089624 A089625 A089626 * A089628 A089629 A089630
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 31 2003
|
| |
|
|
