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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 03:50 EDT 2019. Contains 321450 sequences. (Running on oeis4.)