A291117 - OEIS

A291117

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

1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 7, 8, 4, 1, 1, 15, 30, 20, 7, 1, 1, 31, 104, 102, 46, 11, 1, 1, 63, 342, 496, 300, 96, 16, 1, 1, 127, 1088, 2294, 1891, 786, 183, 22, 1, 1, 255, 3390, 10200, 11417, 6167, 1862, 323, 29, 1, 1, 511, 10424, 44062, 66256, 46417, 17801, 4040, 535, 37, 1, 1, 1023, 31782, 186416, 372190, 336022, 162372, 46425, 8127, 841, 46, 1

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OFFSET

0,7

LINKS

Table of n, a(n) for n=0..76.

M. Griffiths and 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, Mathematics Stack Exchange.

Marko Riedel, Maple code for sequences A241500, A291117, A291118, A291119, A291120.

FORMULA

Formula including proof is at web link.

EXAMPLE

Triangle begins: