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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
OFFSET
0,2
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
KEYWORD
nonn,tabf
AUTHOR
Marko Riedel, Aug 17 2017
STATUS
approved