A122176 Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 1, n-k) for n>=k>=0.

1, 2, 1, 3, 3, 1, 4, 6, 5, 1, 5, 10, 15, 8, 1, 6, 15, 35, 36, 12, 1, 7, 21, 70, 120, 78, 17, 1, 8, 28, 126, 330, 364, 153, 23, 1, 9, 36, 210, 792, 1365, 969, 276, 30, 1, 10, 45, 330, 1716, 4368, 4845, 2300, 465, 38, 1, 11, 55, 495, 3432, 12376, 20349, 14950, 4960, 741, 47, 1

Offset: 0

Author

Paul D. Hanna, Aug 25 2006

Keywords

• nonn
• tabl

Comments

Remarkably, column k of the matrix inverse (A121436) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 2).

Examples

			Triangle begins:
1;
2, 1;
3, 3, 1;
4, 6, 5, 1;
5, 10, 15, 8, 1;
6, 15, 35, 36, 12, 1;
7, 21, 70, 120, 78, 17, 1;
8, 28, 126, 330, 364, 153, 23, 1;
9, 36, 210, 792, 1365, 969, 276, 30, 1; ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A121436 (inverse); variants: A098568, A122175, A122177.

Programs

Mathematica

Flatten[Table[Binomial[(k(k+1))/2+n-k+1,n-k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Mar 18 2013 *)

PARI

T(n,k)=if(n