A107867 Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+1,n-k).

1, 2, 1, 6, 3, 1, 35, 15, 4, 1, 330, 120, 28, 5, 1, 4368, 1365, 286, 45, 6, 1, 74613, 20349, 3876, 560, 66, 7, 1, 1560780, 376740, 65780, 8855, 969, 91, 8, 1, 38608020, 8347680, 1344904, 169911, 17550, 1540, 120, 9, 1, 1101716330, 215553195, 32224114

Offset: 0

Author

Paul D. Hanna, Jun 04 2005

Keywords

• nonn
• tabl

Comments

Remarkably, the following matrix products are all equal to A107876: A107862^-1*A107867 = A107867^-1*A107870 = A107870^-1*A107873.

Examples

			Triangle begins:
1;
2,1;
6,3,1;
35,15,4,1;
330,120,28,5,1;
4368,1365,286,45,6,1;
74613,20349,3876,560,66,7,1;
1560780,376740,65780,8855,969,91,8,1; ...
		

Crossrefs

Cf. A099121, A107862, A107865, A107867, A107870, A107876.

Programs

PARI

T(n,k)=binomial(n*(n-1)/2-k*(k-1)/2 +n-k+1,n-k)