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%I #7 Mar 27 2018 16:29:30
%S 1,1,1,1,3,19,1,5,33,239,1,7,51,387,3011,1,9,73,587,4737,38435,1,11,
%T 99,847,7123,59523,496365,1,13,129,1175,10321,89055,761121,6470385,1,
%U 15,163,1579,14499,129367,1135005,9854211,84975315
%N Rectangular array A(n, k) = (-1)^k*hypergeom([-k, k + n/2 - 1/2], [1], 4) with row n >= 0 and k >= 0, read by ascending antidiagonals.
%e Array starts:
%e [0] 1, 1, 19, 239, 3011, 38435, 496365, 6470385, ... [A299864]
%e [1] 1, 3, 33, 387, 4737, 59523, 761121, 9854211, ... [A299507]
%e [2] 1, 5, 51, 587, 7123, 89055, 1135005, 14660805, ... [A245926]
%e [3] 1, 7, 73, 847, 10321, 129367, 1651609, 21360031, ... [A084768]
%e [4] 1, 9, 99, 1175, 14499, 183195, 2351805, 30539241, ... [A245927]
%e [5] 1, 11, 129, 1579, 19841, 253707, 3284737, 42924203, ...
%e [6] 1, 13, 163, 2067, 26547, 344535, 4508877, 59402397, ...
%t Arow[n_, len_] := Table[(-1)^k Hypergeometric2F1[-k, k + n/2 - 1/2, 1, 4], {k, 0, len}]; Table[Print[Arow[n, 7]], {n, 0, 6}];
%Y Cf. A299864, A299507, A245926, A084768, A245927.
%Y Cf. A300945.
%K nonn,tabl
%O 0,5
%A _Peter Luschny_, Mar 16 2018
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