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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.

%I A291119 #14 Aug 18 2017 23:29:10
%S A291119 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,
%T A291119 1,47,237,361,265,128,47,11,1,1,95,756,1634,1533,847,337,97,16,1,1,
%U A291119 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
%N 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.
%H A291119 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 A291119 Marko Riedel, <a href="https://math.stackexchange.com/questions/2386814/">Partitions into bounded blocks.</a>
%F A291119 Formula including proof is at web link.
%e A291119 Triangle begins:
%e A291119 1,  2,   1,    1;
%e A291119 1,  2,   2,    1,    1;
%e A291119 1,  5,   6,    4,    2,   1;
%e A291119 1, 11,  21,   17,    9,   4,   1;
%e A291119 1, 23,  72,   78,   47,  21,   7,  1;
%e A291119 1, 47, 237,  361,  265, 128,  47, 11,  1;
%e A291119 1, 95, 756, 1634, 1533, 847, 337, 97, 16, 1;
%Y A291119 Cf. A241500, A291117, A291118, A291120.
%K A291119 nonn,tabf
%O A291119 0,2
%A A291119 _Marko Riedel_, Aug 17 2017