A342311 T(n, k) = (n - k + 2)*binomial(2*n, n + k - 2). Triangle read by rows, T(n, k) for 0 <= k <= n.
0, 0, 2, 4, 12, 12, 30, 60, 60, 30, 168, 280, 280, 168, 56, 840, 1260, 1260, 840, 360, 90, 3960, 5544, 5544, 3960, 1980, 660, 132, 18018, 24024, 24024, 18018, 10010, 4004, 1092, 182, 80080, 102960, 102960, 80080, 48048, 21840, 7280, 1680, 240
Offset: 0
Examples
[0] 0 [1] 0, 2 [2] 4, 12, 12 [3] 30, 60, 60, 30 [4] 168, 280, 280, 168, 56 [5] 840, 1260, 1260, 840, 360, 90 [6] 3960, 5544, 5544, 3960, 1980, 660, 132 [7] 18018, 24024, 24024, 18018, 10010, 4004, 1092, 182 [8] 80080, 102960, 102960, 80080, 48048, 21840, 7280, 1680, 240 [9] 350064, 437580, 437580, 350064, 222768, 111384, 42840, 12240, 2448, 306
Programs
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Maple
T := (n, k) -> (n - k + 2)*binomial(2*n, n + k - 2): seq(seq(T(n, k), k=0..n), n=0..9);