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Number of non-isomorphic multiset partitions of weight n in which (1) all parts have the same size and (2) each vertex appears the same number of times.
47

%I #24 Feb 03 2022 16:43:49

%S 1,1,4,4,10,4,21,4,26,13,28,4,128,4,39,84,150,4,358,4,956,513,86,4,

%T 12549,1864,134,9582,52366,4,301086,4,1042038,407140,336,4690369,

%U 61738312,4,532,28011397,2674943885,4,819150246,4,54904825372,65666759973,1303,4,4319823776760

%N Number of non-isomorphic multiset partitions of weight n in which (1) all parts have the same size and (2) each vertex appears the same number of times.

%C a(p) = 4 for p prime. - _Charlie Neder_, Oct 15 2018

%H Andrew Howroyd, <a href="/A319056/b319056.txt">Table of n, a(n) for n = 0..75</a>

%e Non-isomorphic representatives of the a(1) = 1 through a(6) = 21 multiset partitions:

%e (1) (11) (111) (1111) (11111) (111111)

%e (12) (123) (1122) (12345) (111222)

%e (1)(1) (1)(1)(1) (1234) (1)(1)(1)(1)(1) (112233)

%e (1)(2) (1)(2)(3) (11)(11) (1)(2)(3)(4)(5) (123456)

%e (11)(22) (111)(111)

%e (12)(12) (111)(222)

%e (12)(34) (112)(122)

%e (1)(1)(1)(1) (112)(233)

%e (1)(1)(2)(2) (123)(123)

%e (1)(2)(3)(4) (123)(456)

%e (11)(11)(11)

%e (11)(12)(22)

%e (11)(22)(33)

%e (11)(23)(23)

%e (12)(12)(12)

%e (12)(13)(23)

%e (12)(34)(56)

%e (1)(1)(1)(1)(1)(1)

%e (1)(1)(1)(2)(2)(2)

%e (1)(1)(2)(2)(3)(3)

%e (1)(2)(3)(4)(5)(6)

%Y Row sums of A322789.

%Y Cf. A007716, A049311, A064573, A279787, A283877, A306017, A316980, A316981, A316983, A319616.

%K nonn

%O 0,3

%A _Gus Wiseman_, Oct 10 2018

%E Terms a(12) and beyond from _Andrew Howroyd_, Feb 03 2022