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%I #11 Mar 08 2020 06:54:56
%S 1,3,1,15,5,1,35,35,7,1,315,105,63,9,1,693,1155,231,99,11,1,3003,3003,
%T 3003,429,143,13,1,6435,15015,9009,6435,715,195,15,1,109395,36465,
%U 51051,21879,12155,1105,255,17,1,230945,692835,138567,138567,46189,20995,1615,323,19,1
%N 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.
%e Triangle starts:
%e [1]
%e [3, 1]
%e [15, 5, 1]
%e [35, 35, 7, 1]
%e [315, 105, 63, 9, 1]
%e [693, 1155, 231, 99, 11, 1]
%e [3003, 3003, 3003, 429, 143, 13, 1]
%e [6435, 15015, 9009, 6435, 715, 195, 15, 1]
%o (Sage)
%o A269950 = lambda n,k: binomial(1/2,n-k).denom()*binomial(n+1/2,k+1/2)
%o for n in range(8): print([A269950(n,k) for k in (0..n)])
%Y Cf. A001803 (col. 0), A161199 (col. 1), A161201 (col. 2).
%Y Cf. A269949.
%K nonn,tabl
%O 0,2
%A _Peter Luschny_, Apr 07 2016
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