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A291118 Triangle read by rows: T(n,k) number of ways of partitioning the (n+3)-element multiset {1,1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 3.

%I A291118 #16 Aug 18 2017 23:27:33
%S A291118 1,1,1,1,2,1,1,1,4,4,2,1,1,9,14,9,4,1,1,19,49,43,21,7,1,1,39,164,206,
%T A291118 123,47,11,1,1,79,529,957,741,331,97,16,1,1,159,1664,4294,4409,2397,
%U A291118 829,184,22,1,1,319,5149,18713,25551,17353,7105,1919,324,29,1,1,639,15764,79746,144043,123523,60795,19405,4113,536,37,1,1,1279,47929,334237,792561,859327,514081,193530,49002,8218,842,46,1
%N A291118 Triangle read by rows: T(n,k) number of ways of partitioning the (n+3)-element multiset {1,1,1,1,2,3,...,n} into exactly k nonempty parts, n >= 0 and 1 <= k <= n + 3.
%H A291118 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 A291118 Marko Riedel, <a href="https://math.stackexchange.com/questions/2386814/">Partitions into bounded blocks.</a>
%F A291118 Formula including proof is at web link.
%e A291118 Triangle begins:
%e A291118 1,   1,    1;
%e A291118 1,   2,    1,    1;
%e A291118 1,   4,    4,    2,    1;
%e A291118 1,   9,   14,    9,    4,    1;
%e A291118 1,  19,   49,   43,   21,    7,   1;
%e A291118 1,  39,  164,  206,  123,   47,  11,   1;
%e A291118 1,  79,  529,  957,  741,  331,  97,  16,  1;
%e A291118 1, 159, 1664, 4294, 4409, 2397, 829, 184, 22, 1;
%Y A291118 Cf. A241500, A291117, A291119, A291120.
%K A291118 nonn,tabf
%O A291118 0,5
%A A291118 _Marko Riedel_, Aug 17 2017