A107870 Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+2, n-k).

1, 3, 1, 10, 4, 1, 56, 21, 5, 1, 495, 165, 36, 6, 1, 6188, 1820, 364, 55, 7, 1, 100947, 26334, 4845, 680, 78, 8, 1, 2035800, 475020, 80730, 10626, 1140, 105, 9, 1, 48903492, 10295472, 1623160, 201376, 20475, 1771, 136, 10, 1, 1362649145, 260932815

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;
3,1;
10,4,1;
56,21,5,1;
495,165,36,6,1;
6188,1820,364,55,7,1;
100947,26334,4845,680,78,8,1;
2035800,475020,80730,10626,1140,105,9,1; ...
		

Crossrefs

Cf. A107862, A107865, A107867, A107876, A107871, A107872.

Programs

PARI

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