A121334 Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k, n-k), for n>=k>=0.

1, 2, 1, 10, 4, 1, 84, 28, 7, 1, 1001, 286, 66, 11, 1, 15504, 3876, 816, 136, 16, 1, 296010, 65780, 12650, 2024, 253, 22, 1, 6724520, 1344904, 237336, 35960, 4495, 435, 29, 1, 177232627, 32224114, 5245786, 749398, 91390, 9139, 703, 37, 1, 5317936260

Offset: 0

Author

Paul D. Hanna, Aug 29 2006

Keywords

• nonn
• tabl

Comments

A triangle having similar properties and complementary construction is the dual triangle A122175.

Examples

			Triangle begins:
1;
2, 1;
10, 4, 1;
84, 28, 7, 1;
1001, 286, 66, 11, 1;
15504, 3876, 816, 136, 16, 1;
296010, 65780, 12650, 2024, 253, 22, 1;
6724520, 1344904, 237336, 35960, 4495, 435, 29, 1;
177232627, 32224114, 5245786, 749398, 91390, 9139, 703, 37, 1; ...
		

Crossrefs

Cf. A121439 (matrix inverse); A121412; variants: A122178, A121335, A121336; A122175 (dual).

Programs

PARI

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

Formula

Remarkably, row n of the matrix inverse (A121439) equals row n of A121412^(-n*(n+1)/2-1). Further, the following matrix products of triangles of binomial coefficients are equal: A121412 = A121334*A122178^-1 = A121335*A121334^-1 = A121336*A121335^-1, where row n of H=A121412 equals row (n-1) of H^(n+1) with an appended '1'.