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.
1, 1, 1, 1, 3, 19, 1, 5, 33, 239, 1, 7, 51, 387, 3011, 1, 9, 73, 587, 4737, 38435, 1, 11, 99, 847, 7123, 59523, 496365, 1, 13, 129, 1175, 10321, 89055, 761121, 6470385, 1, 15, 163, 1579, 14499, 129367, 1135005, 9854211, 84975315
Offset: 0
Examples
Array starts: [0] 1, 1, 19, 239, 3011, 38435, 496365, 6470385, ... [A299864] [1] 1, 3, 33, 387, 4737, 59523, 761121, 9854211, ... [A299507] [2] 1, 5, 51, 587, 7123, 89055, 1135005, 14660805, ... [A245926] [3] 1, 7, 73, 847, 10321, 129367, 1651609, 21360031, ... [A084768] [4] 1, 9, 99, 1175, 14499, 183195, 2351805, 30539241, ... [A245927] [5] 1, 11, 129, 1579, 19841, 253707, 3284737, 42924203, ... [6] 1, 13, 163, 2067, 26547, 344535, 4508877, 59402397, ...
Programs
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Mathematica
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}];