A337995 T(n, k) = A337994(n, k) / A099398(n). Triangle read by rows, for 0 <= k <= n.
1, 0, 2, 0, 3, 15, 0, 6, 30, 84, 0, 2, 10, 28, 60, 0, 12, 60, 168, 360, 660, 0, 3, 15, 42, 90, 165, 273, 0, 2, 10, 28, 60, 110, 182, 280, 0, 6, 30, 84, 180, 330, 546, 840, 1224, 0, 12, 60, 168, 360, 660, 1092, 1680, 2448, 3420, 0, 2, 10, 28, 60, 110, 182, 280, 408, 570, 770
Offset: 0
Examples
Triangle starts: [0] 1 [1] 0, 2 [2] 0, 3, 15 [3] 0, 6, 30, 84 [4] 0, 2, 10, 28, 60 [5] 0, 12, 60, 168, 360, 660 [6] 0, 3, 15, 42, 90, 165, 273 [7] 0, 2, 10, 28, 60, 110, 182, 280 [8] 0, 6, 30, 84, 180, 330, 546, 840, 1224 [9] 0, 12, 60, 168, 360, 660, 1092, 1680, 2448, 3420
Programs
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Maple
T := (n, k) -> `if`(n=0, 1, (k*(2*k+2)*(2*k+1)*(2*n-1)*binomial(2*(n-1),n-1))/(n*(n+1)*(n+2))/numer((2^(1-2*n)*binomial(2*n,n))/((n+1)*(n+2)))): seq(seq(T(n, k), k=0..n), n=0..10);