A291117 Triangle read by rows: T(n,k) = number of ways of partitioning the (n+2)-element multiset {1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 2.

1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 7, 8, 4, 1, 1, 15, 30, 20, 7, 1, 1, 31, 104, 102, 46, 11, 1, 1, 63, 342, 496, 300, 96, 16, 1, 1, 127, 1088, 2294, 1891, 786, 183, 22, 1, 1, 255, 3390, 10200, 11417, 6167, 1862, 323, 29, 1, 1, 511, 10424, 44062, 66256, 46417, 17801, 4040, 535, 37, 1, 1, 1023, 31782, 186416, 372190, 336022, 162372, 46425, 8127, 841, 46, 1

Offset: 0

Author

Marko Riedel, Aug 17 2017

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1,   1;
  1,   1,   1;
  1,   3,   2,   1;
  1,   7,   8,   4,   1;
  1,  15,  30,  20,   7,  1;
  1,  31, 104, 102,  46, 11,  1;
  1,  63, 342, 496, 300, 96, 16, 1;
		

Links

• M. Griffiths and I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5.
• Marko Riedel, Partitions into bounded blocks, Mathematics Stack Exchange.
• Marko Riedel, Maple code for sequences A241500, A291117, A291118, A291119, A291120.

Crossrefs

Cf. A241500, A291118, A291119, A291120.

Columns k=1..4: A000012, A255047, A168605, A168606.

Formula

Formula including proof is at web link.