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%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
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