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

0,7

Links

Table of n, a(n) for n=0..76.

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.

Formula

Formula including proof is at web link.

Example

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;

Crossrefs

Cf. A241500, A291118, A291119, A291120.

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

Sequence in context: A118654 A111760 A078424 * A293181 A229345 A240235

Adjacent sequences: A291114 A291115 A291116 * A291118 A291119 A291120

Keyword

nonn,tabf

Author

Marko Riedel, Aug 17 2017

Status

approved