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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

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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;