A367024 - OEIS

%I #9 Nov 07 2023 14:43:18

%S -1,-1,2,-1,8,2,-1,18,18,4,-1,32,72,64,10,-1,50,200,400,250,28,-1,72,

%T 450,1600,2250,1008,84,-1,98,882,4900,12250,12348,4116,264,-1,128,

%U 1568,12544,49000,87808,65856,16896,858,-1,162,2592,28224,158760,444528,592704,342144,69498,2860

%N Triangle read by rows, T(n, k) = [x^k] -hypergeom([-1/2, -n, -n], [1, 1], 4*x).

%F T(n, k) = binomial(n, k)^2 * binomial(2*k, k) / (2*k - 1).

%e Triangle T(n, k) starts:

%e   [0] -1;

%e   [1] -1,   2;

%e   [2] -1,   8,    2;

%e   [3] -1,  18,   18,     4;

%e   [4] -1,  32,   72,    64,     10;

%e   [5] -1,  50,  200,   400,    250,     28;

%e   [6] -1,  72,  450,  1600,   2250,   1008,     84;

%e   [7] -1,  98,  882,  4900,  12250,  12348,   4116,    264;

%e   [8] -1, 128, 1568, 12544,  49000,  87808,  65856,  16896,   858;

%e   [9] -1, 162, 2592, 28224, 158760, 444528, 592704, 342144, 69498, 2860;

%p p := n -> -hypergeom([-1/2, -n, -n], [1, 1], 4*x):

%p T := (n, k) -> coeff(simplify(p(n)), x, k):

%p seq(seq(T(n, k), k = 0..n), n = 0..9);

%Y Cf. A246065 (row sums), -A002420 and A284016 (main diagonal).

%Y Cf. A367022, A367023, A387025.

%K sign,tabl

%O 0,3

%A _Peter Luschny_, Nov 07 2023