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%I #20 Sep 08 2022 08:46:10
%S 1,1,1,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,
%T 1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,
%U 1,1,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1
%N Triangle read by rows: T(n,k) = {binomial(n+k,n-k)*binomial(n,k)} mod 2, 0 <= k <= n.
%C Row sums give A106737.
%H Chai Wah Wu, <a href="/A253084/b253084.txt">Table of n, a(n) for n = 0..10010</a>
%F T(n,k) = 1 if and only if ((n-k) AND NOT (n+k)) OR (k AND NOT n) is zero where AND, OR and NOT are bitwise operators. - _Chai Wah Wu_, Feb 09 2016
%e Triangle begins:
%e [1]
%e [1, 1]
%e [1, 0, 1]
%e [1, 0, 1, 1]
%e [1, 0, 0, 0, 1]
%e [1, 1, 0, 0, 1, 1]
%e [1, 0, 0, 0, 1, 0, 1]
%e [1, 0, 0, 0, 1, 0, 1, 1]
%e [1, 0, 0, 0, 0, 0, 0, 0, 1]
%e [1, 1, 0, 0, 0, 0, 0, 0, 1, 1]
%e [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]
%e [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]
%e [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
%e ...
%t Table[Mod[Binomial[n + k, n - k] Binomial[n, k], 2], {n, 0, 13}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Feb 10 2016 *)
%o (PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1((binomial(n+k,n-k)*binomial(n,k)) % 2, ", ");); print(););} \\ _Michel Marcus_, Feb 06 2015
%o (Python)
%o def A253084_T(n,k):
%o return int(not (~(n+k) & (n-k)) | (~n & k)) # _Chai Wah Wu_, Feb 09 2016
%o (Magma) /* As triangle */ [[Binomial(n+k,n-k)*Binomial(n,k) mod 2: k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Feb 10 2016
%Y Cf. A082759, A106737.
%K nonn,tabl
%O 0
%A _N. J. A. Sloane_, Feb 05 2015
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