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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.

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