A291118 Triangle read by rows: T(n,k) number of ways of partitioning the (n+3)-element multiset {1,1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 3.

1, 1, 1, 1, 2, 1, 1, 1, 4, 4, 2, 1, 1, 9, 14, 9, 4, 1, 1, 19, 49, 43, 21, 7, 1, 1, 39, 164, 206, 123, 47, 11, 1, 1, 79, 529, 957, 741, 331, 97, 16, 1, 1, 159, 1664, 4294, 4409, 2397, 829, 184, 22, 1, 1, 319, 5149, 18713, 25551, 17353, 7105, 1919, 324, 29, 1, 1, 639, 15764, 79746, 144043, 123523, 60795, 19405, 4113, 536, 37, 1, 1, 1279, 47929, 334237, 792561, 859327, 514081, 193530, 49002, 8218, 842, 46, 1

Offset

0,5

Links

Table of n, a(n) for n=0..87.

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,   1,    1;
1,   2,    1,    1;
1,   4,    4,    2,    1;
1,   9,   14,    9,    4,    1;
1,  19,   49,   43,   21,    7,   1;
1,  39,  164,  206,  123,   47,  11,   1;
1,  79,  529,  957,  741,  331,  97,  16,  1;
1, 159, 1664, 4294, 4409, 2397, 829, 184, 22, 1;

Crossrefs

Cf. A241500, A291117, A291119, A291120.

Sequence in context: A219094 A362824 A213268 * A245184 A284414 A355614

Adjacent sequences: A291115 A291116 A291117 * A291119 A291120 A291121

Keyword

nonn,tabf

Author

Marko Riedel, Aug 17 2017

Status

approved