A379100 Triangle read by rows: T(n, k) = binomial(2*k, k) * binomial(2*n, n) / (n + 1).
1, 1, 2, 2, 4, 12, 5, 10, 30, 100, 14, 28, 84, 280, 980, 42, 84, 252, 840, 2940, 10584, 132, 264, 792, 2640, 9240, 33264, 121968, 429, 858, 2574, 8580, 30030, 108108, 396396, 1472328, 1430, 2860, 8580, 28600, 100100, 360360, 1321320, 4907760, 18404100
Offset: 0
Examples
[0] 1; [1] 1, 2; [2] 2, 4, 12; [3] 5, 10, 30, 100; [4] 14, 28, 84, 280, 980; [5] 42, 84, 252, 840, 2940, 10584; [6] 132, 264, 792, 2640, 9240, 33264, 121968; [7] 429, 858, 2574, 8580, 30030, 108108, 396396, 1472328;
Programs
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Maple
T := (n, k) -> binomial(2*k, k) * binomial(2*n, n) / (n + 1): seq(seq(T(n, k), k = 0..n), n = 0..8);
Formula
T(n, k) = ((2*k)! * (2*n)!) / ((k! * n!)^2 * (n+1)).