A291119 Triangle read by rows: T(n,k) number of ways of partitioning the (n+4)-element multiset {1,1,1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 4.

1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 5, 6, 4, 2, 1, 1, 11, 21, 17, 9, 4, 1, 1, 23, 72, 78, 47, 21, 7, 1, 1, 47, 237, 361, 265, 128, 47, 11, 1, 1, 95, 756, 1634, 1533, 847, 337, 97, 16, 1, 1, 191, 2361, 7197, 8819, 5826, 2571, 836, 184, 22, 1, 1, 383, 7272, 30958, 49807, 40433, 20419, 7372, 1927, 324, 29, 1, 1, 767, 22197, 130721, 275445, 278380, 165103, 66809, 19794, 4122, 536, 37, 1

Offset

0,2

Links

Table of n, a(n) for n=0..84.

M. Griffiths, 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.

Formula

Formula including proof is at web link.

Example

Triangle begins:
1,  2,   1,    1;
1,  2,   2,    1,    1;
1,  5,   6,    4,    2,   1;
1, 11,  21,   17,    9,   4,   1;
1, 23,  72,   78,   47,  21,   7,  1;
1, 47, 237,  361,  265, 128,  47, 11,  1;
1, 95, 756, 1634, 1533, 847, 337, 97, 16, 1;

Crossrefs

Cf. A241500, A291117, A291118, A291120.

Sequence in context: A322596 A037306 A194799 * A366309 A007424 A369163

Adjacent sequences: A291116 A291117 A291118 * A291120 A291121 A291122

Keyword

nonn,tabf

Author

Marko Riedel, Aug 17 2017

Status

approved