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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
OFFSET
0,4
COMMENTS
Numerators of "gravitational descendent fields" presented on p. 28 of the Zhou reference. See also p. 31. - Tom Copeland, Feb 13 2017
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Apr 07 2016
STATUS
approved