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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..54.

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

EXAMPLE

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]

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 *)

PROG

(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)]

CROSSREFS

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

Cf. A269950.

Sequence in context: A209583 A144944 A137426 * A074456 A016454 A065227

Adjacent sequences:  A269946 A269947 A269948 * A269950 A269951 A269952

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 07 2016

STATUS

approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)