A291120 Triangle read by rows: T(n,k) number of ways of partitioning the (n+5)-element multiset {1,1,1,1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 5.

1, 2, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 6, 9, 7, 4, 2, 1, 1, 13, 30, 29, 18, 9, 4, 1, 1, 27, 100, 129, 92, 48, 21, 7, 1, 1, 55, 324, 581, 504, 287, 129, 47, 11, 1, 1, 111, 1024, 2577, 2834, 1844, 879, 338, 97, 16, 1, 1, 223, 3180, 11189, 15918, 12301, 6431, 2615, 837, 184, 22, 1, 1, 447, 9760, 47649, 88232, 83050, 49197, 21498, 7430, 1928, 324, 29, 1, 1, 895, 29724, 199781, 481044, 558819, 384913, 184823, 68606, 19868, 4123, 536, 37, 1

Offset

0,2

Links

Table of n, a(n) for n=0..94.

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,    2,    1,    1;
1,   3,    3,    2,    1,    1;
1,   6,    9,    7,    4,    2,   1;
1,  13,   30,   29,   18,    9,   4,   1;
1,  27,  100,  129,   92,   48,  21,   7,  1;
1,  55,  324,  581,  504,  287, 129,  47, 11,  1;
1, 111, 1024, 2577, 2834, 1844, 879, 338, 97, 16, 1;

Crossrefs

Cf. A241500, A291117, A291118, A291119.

Sequence in context: A134513 A275648 A201881 * A025485 A219365 A140751

Adjacent sequences: A291117 A291118 A291119 * A291121 A291122 A291123

Keyword

nonn,tabf

Author

Marko Riedel, Aug 17 2017

Status

approved