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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.

%I A291120 #16 Aug 18 2017 23:31:09
%S A291120 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,
%T A291120 92,48,21,7,1,1,55,324,581,504,287,129,47,11,1,1,111,1024,2577,2834,
%U A291120 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
%N 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.
%H A291120 M. Griffiths, I. Mezo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Griffiths/griffiths11.html">A generalization of Stirling Numbers of the Second Kind via a special multiset</a>, JIS 13 (2010) #10.2.5
%H A291120 Marko Riedel, <a href="https://math.stackexchange.com/questions/2386814/">Partitions into bounded blocks.</a>
%F A291120 Formula including proof is at web link.
%e A291120 Triangle begins:
%e A291120 1,   2,    2,    1,    1;
%e A291120 1,   3,    3,    2,    1,    1;
%e A291120 1,   6,    9,    7,    4,    2,   1;
%e A291120 1,  13,   30,   29,   18,    9,   4,   1;
%e A291120 1,  27,  100,  129,   92,   48,  21,   7,  1;
%e A291120 1,  55,  324,  581,  504,  287, 129,  47, 11,  1;
%e A291120 1, 111, 1024, 2577, 2834, 1844, 879, 338, 97, 16, 1;
%Y A291120 Cf. A241500, A291117, A291118, A291119.
%K A291120 nonn,tabf
%O A291120 0,2
%A A291120 _Marko Riedel_, Aug 17 2017