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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.

%I A291117 #34 Aug 12 2022 09:17:59
%S A291117 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,
%T A291117 342,496,300,96,16,1,1,127,1088,2294,1891,786,183,22,1,1,255,3390,
%U A291117 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
%N 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.
%H A291117 M. Griffiths and 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 A291117 Marko Riedel, <a href="https://math.stackexchange.com/questions/2386814/">Partitions into bounded blocks</a>, Mathematics Stack Exchange.
%H A291117 Marko Riedel, <a href="/A291117/a291117_2.maple.txt">Maple code for sequences A241500, A291117, A291118, A291119, A291120.</a>
%F A291117 Formula including proof is at web link.
%e A291117 Triangle begins:
%e A291117   1,   1;
%e A291117   1,   1,   1;
%e A291117   1,   3,   2,   1;
%e A291117   1,   7,   8,   4,   1;
%e A291117   1,  15,  30,  20,   7,  1;
%e A291117   1,  31, 104, 102,  46, 11,  1;
%e A291117   1,  63, 342, 496, 300, 96, 16, 1;
%Y A291117 Cf. A241500, A291118, A291119, A291120.
%Y A291117 Columns k=1..4: A000012, A255047, A168605, A168606.
%K A291117 nonn,tabf
%O A291117 0,7
%A A291117 _Marko Riedel_, Aug 17 2017