A349727 Triangle read by rows, T(n, k) = [x^(n - k)] hypergeom([-n, -1 + n], [-n], x).
1, 0, 1, 1, 1, 1, 4, 3, 2, 1, 15, 10, 6, 3, 1, 56, 35, 20, 10, 4, 1, 210, 126, 70, 35, 15, 5, 1, 792, 462, 252, 126, 56, 21, 6, 1, 3003, 1716, 924, 462, 210, 84, 28, 7, 1, 11440, 6435, 3432, 1716, 792, 330, 120, 36, 8, 1, 43758, 24310, 12870, 6435, 3003, 1287, 495, 165, 45, 9, 1
Offset: 0
Examples
Triangle starts: [0] 1; [1] 0, 1; [2] 1, 1, 1; [3] 4, 3, 2, 1; [4] 15, 10, 6, 3, 1; [5] 56, 35, 20, 10, 4, 1; [6] 210, 126, 70, 35, 15, 5, 1; [7] 792, 462, 252, 126, 56, 21, 6, 1; [8] 3003, 1716, 924, 462, 210, 84, 28, 7, 1; [9] 11440, 6435, 3432, 1716, 792, 330, 120, 36, 8, 1;
Crossrefs
Programs
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Maple
p := n -> hypergeom([-n, -1 + n], [-n], x): seq(seq(coeff(simplify(p(n)), x, n - k), k = 0..n), n = 0..10);
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Mathematica
(* rows[0..k], k[0..oo] *) r={};k=11;For[n=0,n