A140880 Triangle read by rows, T(n,k) = Gamma(n+3)/(Gamma(k+1)*Gamma(n-k+1)) for n>=0 and 0<=k<=n.

2, 6, 6, 12, 24, 12, 20, 60, 60, 20, 30, 120, 180, 120, 30, 42, 210, 420, 420, 210, 42, 56, 336, 840, 1120, 840, 336, 56, 72, 504, 1512, 2520, 2520, 1512, 504, 72, 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Jul 22 2008

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 2
[1] 6,    6
[2] 12,  24,   12
[3] 20,  60,   60,   20
[4] 30, 120,  180,  120,   30
[5] 42, 210,  420,  420,  210,   42
[6] 56, 336,  840, 1120,  840,  336,   56
[7] 72, 504, 1512, 2520, 2520, 1512,  504,  72
[8] 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90
		

Crossrefs

T(n,0) = T(n,n) = A002378(n+1). T(n,k) = 2*A094305(n,k).

Row sums are A001815(n+2).

Cf. A007318.

Programs

Maple

T := (n,k) -> GAMMA(n+3)/(GAMMA(k+1)*GAMMA(n-k+1)):
seq(seq(T(n,k), k=0..n), n=0..8); # Peter Luschny, Oct 29 2017

Mathematica

Flatten[Table[Gamma[n+3]/(Gamma[k+1]Gamma[n-k+1]),{n,0,8},{k,0,n}]]

Extensions

Edited and new name from Peter Luschny, Oct 29 2017