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A300946 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.

%I A300946 #7 Mar 27 2018 16:29:30
%S A300946 1,1,1,1,3,19,1,5,33,239,1,7,51,387,3011,1,9,73,587,4737,38435,1,11,
%T A300946 99,847,7123,59523,496365,1,13,129,1175,10321,89055,761121,6470385,1,
%U A300946 15,163,1579,14499,129367,1135005,9854211,84975315
%N A300946 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 A300946 Array starts:
%e A300946 [0] 1,  1,  19,  239,  3011,  38435,  496365,  6470385, ... [A299864]
%e A300946 [1] 1,  3,  33,  387,  4737,  59523,  761121,  9854211, ... [A299507]
%e A300946 [2] 1,  5,  51,  587,  7123,  89055, 1135005, 14660805, ... [A245926]
%e A300946 [3] 1,  7,  73,  847, 10321, 129367, 1651609, 21360031, ... [A084768]
%e A300946 [4] 1,  9,  99, 1175, 14499, 183195, 2351805, 30539241, ... [A245927]
%e A300946 [5] 1, 11, 129, 1579, 19841, 253707, 3284737, 42924203, ...
%e A300946 [6] 1, 13, 163, 2067, 26547, 344535, 4508877, 59402397, ...
%t A300946 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 A300946 Cf. A299864, A299507, A245926, A084768, A245927.
%Y A300946 Cf. A300945.
%K A300946 nonn,tabl
%O A300946 0,5
%A A300946 _Peter Luschny_, Mar 16 2018