A367024 Triangle read by rows, T(n, k) = [x^k] -hypergeom([-1/2, -n, -n], [1, 1], 4*x).
-1, -1, 2, -1, 8, 2, -1, 18, 18, 4, -1, 32, 72, 64, 10, -1, 50, 200, 400, 250, 28, -1, 72, 450, 1600, 2250, 1008, 84, -1, 98, 882, 4900, 12250, 12348, 4116, 264, -1, 128, 1568, 12544, 49000, 87808, 65856, 16896, 858, -1, 162, 2592, 28224, 158760, 444528, 592704, 342144, 69498, 2860
Offset: 0
Examples
Triangle T(n, k) starts: [0] -1; [1] -1, 2; [2] -1, 8, 2; [3] -1, 18, 18, 4; [4] -1, 32, 72, 64, 10; [5] -1, 50, 200, 400, 250, 28; [6] -1, 72, 450, 1600, 2250, 1008, 84; [7] -1, 98, 882, 4900, 12250, 12348, 4116, 264; [8] -1, 128, 1568, 12544, 49000, 87808, 65856, 16896, 858; [9] -1, 162, 2592, 28224, 158760, 444528, 592704, 342144, 69498, 2860;
Crossrefs
Programs
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Maple
p := n -> -hypergeom([-1/2, -n, -n], [1, 1], 4*x): T := (n, k) -> coeff(simplify(p(n)), x, k): seq(seq(T(n, k), k = 0..n), n = 0..9);
Formula
T(n, k) = binomial(n, k)^2 * binomial(2*k, k) / (2*k - 1).