A269950 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, 3, 1, 15, 5, 1, 35, 35, 7, 1, 315, 105, 63, 9, 1, 693, 1155, 231, 99, 11, 1, 3003, 3003, 3003, 429, 143, 13, 1, 6435, 15015, 9009, 6435, 715, 195, 15, 1, 109395, 36465, 51051, 21879, 12155, 1105, 255, 17, 1, 230945, 692835, 138567, 138567, 46189, 20995, 1615, 323, 19, 1

Offset

0,2

Links

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

Example

Triangle starts:
[1]
[3,    1]
[15,   5,     1]
[35,   35,    7,    1]
[315,  105,   63,   9,    1]
[693,  1155,  231,  99,   11,  1]
[3003, 3003,  3003, 429,  143, 13,  1]
[6435, 15015, 9009, 6435, 715, 195, 15, 1]

Prog

(Sage)
A269950 = lambda n, k: binomial(1/2, n-k).denom()*binomial(n+1/2, k+1/2)
for n in range(8): print([A269950(n, k) for k in (0..n)])

Crossrefs

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

Cf. A269949.

Sequence in context: A263917 A324428 A131440 * A190088 A119301 A293157

Adjacent sequences: A269947 A269948 A269949 * A269951 A269952 A269953

Keyword

nonn,tabl

Author

Peter Luschny, Apr 07 2016

Status

approved