A358710 - OEIS

%I #47 Jan 05 2023 18:44:31

%S 1,1,1,1,4,3,1,1,13,26,19,6,1,1,40,183,259,163,55,10,1,1,121,1190,

%T 3115,3373,1896,620,125,15,1,1,364,7443,34891,62240,54774,27610,8706,

%U 1795,245,21,1,1,1093,45626,374059,1072316,1435175,1063570,485850,146363,30261,4361,434,28,1

%N Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 2, 2, ..., n, n] into k nonempty submultisets, for 1 <= k <= 2n.

%C A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=2.

%D F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.

%H Sidney Cadot, <a href="/A358710/b358710.txt">Table of n, a(n) for n = 0..420</a> (terms 1..420 from Marko Riedel)

%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/4585780/">Number of ways to partition a multiset into k non-empty multisets</a>, Mathematics Stack Exchange.

%H Marko Riedel, <a href="/A358710/a358710.maple.txt">Maple code for sequence by plain enumeration, the Polya Enumeration Theorem, and Power Group Enumeration</a>.

%e The triangular array starts:

%e [0] 1;

%e [1] 1,   1;

%e [2] 1,   4,    3,     1;

%e [3] 1,  13,   26,    19,     6,     1;

%e [4] 1,  40,  183,   259,   163,    55,    10,    1;

%e [5] 1, 121, 1190,  3115,  3373,  1896,   620,  125,   15,   1;

%e [6] 1, 364, 7443, 34891, 62240, 54774, 27610, 8706, 1795, 245, 21, 1;

%Y Cf. A008277, A020555 (row sums), A358721, A358722.

%K nonn,tabf

%O 0,5

%A _Marko Riedel_, Nov 27 2022