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A367024
Triangle read by rows, T(n, k) = [x^k] -hypergeom([-1/2, -n, -n], [1, 1], 4*x).
0
-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
0,3
FORMULA
T(n, k) = binomial(n, k)^2 * binomial(2*k, k) / (2*k - 1).
EXAMPLE
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;
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);
CROSSREFS
Cf. A246065 (row sums), -A002420 and A284016 (main diagonal).
Sequence in context: A180956 A208921 A208660 * A114706 A046740 A317932
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Nov 07 2023
STATUS
approved