A177517 Triangle T(n,k) read by rows defined by recurrence T(n,1)=A000007(n-1) and T(n,k) = sum_{i=1..k-1} T(n-i,k-1) if k>1.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 3, 1, 0, 0, 0, 1, 5, 4, 1, 0, 0, 0, 0, 6, 9, 5, 1, 0, 0, 0, 0, 5, 15, 14, 6, 1, 0, 0, 0, 0, 3, 20, 29, 20, 7, 1, 0, 0, 0, 0, 1, 22, 49, 49, 27, 8, 1, 0, 0, 0, 0, 0, 20, 71, 98, 76, 35, 9, 1, 0, 0, 0, 0, 0, 15, 90, 169, 174, 111, 44, 10, 1, 0, 0, 0, 0, 0, 9, 101, 259, 343, 285, 155, 54, 11, 1, 0, 0, 0, 0, 0, 4, 101, 359, 602, 628, 440, 209, 65, 12, 1, 0, 0, 0, 0, 0, 1, 90, 455, 961, 1230, 1068, 649, 274, 77, 13, 1

Offset: 1

Author

Mats Granvik, Roger L. Bagula, Dec 11 2010

Keywords

• nonn
• tabl

Comments

A008302 is the main entry for this triangle.

Essentially A060701 which is equal to this table beginning from the second column.

The recurrence formula is similar to the recurrence for A177978.

Examples

			1,
0,1,
0,0,1,
0,0,1,1,
0,0,0,2,1,
0,0,0,2,3,1,
0,0,0,1,5,4,1,
0,0,0,0,6,9,5,1,
0,0,0,0,5,15,14,6,1,
0,0,0,0,3,20,29,20,7,1,
0,0,0,0,1,22,49,49,27,8,1
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20301

Crossrefs

Cf. A008302, A060701, A177978, A175105. Column sums are A000142. Row sums are A008930.

Programs

Mathematica

t[1, 1] = 1; t[n_, 1] = 0; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}], 0];
Flatten[Table[t[n, k], {n, 12}, {k, n}]]
(* Robert G. Wilson v, Jun 24 2011 *) (* corrected by Mats Granvik, Jan 23 2012 *)

Formula

T(n,k) = A008302(k-2,n-k), n>=k>1. - R. J. Mathar, Dec 15 2010