A269949 Triangle read by rows, T(n,k) = denominator(binomial(-1/2, n-k))*binomial(n-1/2, k-1/2), for n>=0 and 0<=k<=n.

1, 1, 1, 3, 3, 1, 5, 15, 5, 1, 35, 35, 35, 7, 1, 63, 315, 105, 63, 9, 1, 231, 693, 1155, 231, 99, 11, 1, 429, 3003, 3003, 3003, 429, 143, 13, 1, 6435, 6435, 15015, 9009, 6435, 715, 195, 15, 1, 12155, 109395, 36465, 51051, 21879, 12155, 1105, 255, 17, 1

Offset: 0

Author

Peter Luschny, Apr 07 2016

Keywords

• nonn
• tabl

Comments

Numerators of "gravitational descendent fields" presented on p. 28 of the Zhou reference. See also p. 31. - Tom Copeland, Feb 13 2017

Examples

			Triangle starts:
[  1]
[  1,   1]
[  3,   3,    1]
[  5,  15,    5,   1]
[ 35,  35,   35,   7,  1]
[ 63, 315,  105,  63,  9,  1]
[231, 693, 1155, 231, 99, 11, 1]
		

Links

• J. Zhou, Quantum deformation theory of the Airy curve and the mirror symmetry of a point, arXiv preprint arXiv:1405.5296 [math.AG], 2014.

Crossrefs

Cf. A001790 (col. 0), A001803 (col. 1), A161199 (col. 2), A161201 (col. 3).

Cf. A269950.

Programs

Mathematica

Table[Denominator[Binomial[-1/2, n - k]] Binomial[n - 1/2, k - 1/2], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Feb 13 2017 *)

Sage

A269949 = lambda n,k: binomial(-1/2,n-k).denom()*binomial(n-1/2,k-1/2)
for n in range(8): print([A269949(n,k) for k in (0..n)])