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A299444 Triangle read by rows, T(n, k) = 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2) for n >= 0 and 0 <= k <= n.

%I A299444 #5 Feb 10 2018 15:27:20
%S A299444 1,1,2,1,5,4,1,10,16,8,1,17,49,44,16,1,26,121,182,112,32,1,37,256,593,
%T A299444 584,272,64,1,50,484,1616,2368,1712,640,128,1,65,841,3848,7921,8312,
%U A299444 4720,1472,256,1,82,1369,8254,22841,33002,26704,12448,3328,512
%N A299444 Triangle read by rows, T(n, k) = 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2) for n >= 0 and 0 <= k <= n.
%e A299444 Triangle starts:
%e A299444 [0] 1
%e A299444 [1] 1,  2
%e A299444 [2] 1,  5,    4
%e A299444 [3] 1, 10,   16,    8
%e A299444 [4] 1, 17,   49,   44,   16
%e A299444 [5] 1, 26,  121,  182,  112,     32
%e A299444 [6] 1, 37,  256,  593,  584,    272,    64
%e A299444 [7] 1, 50,  484, 1616, 2368,   1712,   640,   128
%e A299444 [8] 1, 65,  841, 3848, 7921,   8312,  4720,  1472,  256
%e A299444 [9] 1, 82, 1369, 8254, 22841, 33002, 26704, 12448, 3328, 512
%p A299444 T := (n, k) -> 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2):
%p A299444 seq(seq(simplify(T(n,k)), k=0..n), n=0..9);
%Y A299444 Cf. A299443 (row sums).
%K A299444 nonn,tabl
%O A299444 0,3
%A A299444 _Peter Luschny_, Feb 10 2018