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

Author

Peter Luschny, Nov 01 2020

Keywords

• nonn
• tabl

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
		

Crossrefs

Cf. A337994, A099398.

Programs

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);