A121336 Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k + 2, n-k), for n>=k>=0.

1, 4, 1, 21, 6, 1, 165, 45, 9, 1, 1820, 455, 91, 13, 1, 26334, 5985, 1140, 171, 18, 1, 475020, 98280, 17550, 2600, 300, 24, 1, 10295472, 1947792, 324632, 46376, 5456, 496, 31, 1, 260932815, 45379620, 7059052, 962598, 111930, 10660, 780, 39, 1

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 A122177.

Examples

			Triangle begins:
1;
4, 1;
21, 6, 1;
165, 45, 9, 1;
1820, 455, 91, 13, 1;
26334, 5985, 1140, 171, 18, 1;
475020, 98280, 17550, 2600, 300, 24, 1;
10295472, 1947792, 324632, 46376, 5456, 496, 31, 1;
260932815, 45379620, 7059052, 962598, 111930, 10660, 780, 39, 1; ...
		

Crossrefs

Cf. A121441 (matrix inverse); A121412; variants: A122178, A121334, A121335; A122177 (dual).

Programs

PARI

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

Formula

Remarkably, row n of the matrix inverse (A121441) equals row n of A121412^(-n*(n+1)/2-3). 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'.