

A319056


Number of nonisomorphic 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



1, 1, 4, 4, 10, 4, 21, 4, 26, 13, 28, 4, 128, 4, 39, 84, 150, 4, 358, 4, 956, 513, 86, 4, 12549, 1864, 134, 9582, 52366, 4, 301086, 4, 1042038, 407140, 336, 4690369, 61738312, 4, 532, 28011397, 2674943885, 4, 819150246, 4, 54904825372, 65666759973, 1303, 4, 4319823776760
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OFFSET

0,3


COMMENTS

a(p) = 4 for p prime.  Charlie Neder, Oct 15 2018


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..75


EXAMPLE

Nonisomorphic representatives of the a(1) = 1 through a(6) = 21 multiset partitions:
(1) (11) (111) (1111) (11111) (111111)
(12) (123) (1122) (12345) (111222)
(1)(1) (1)(1)(1) (1234) (1)(1)(1)(1)(1) (112233)
(1)(2) (1)(2)(3) (11)(11) (1)(2)(3)(4)(5) (123456)
(11)(22) (111)(111)
(12)(12) (111)(222)
(12)(34) (112)(122)
(1)(1)(1)(1) (112)(233)
(1)(1)(2)(2) (123)(123)
(1)(2)(3)(4) (123)(456)
(11)(11)(11)
(11)(12)(22)
(11)(22)(33)
(11)(23)(23)
(12)(12)(12)
(12)(13)(23)
(12)(34)(56)
(1)(1)(1)(1)(1)(1)
(1)(1)(1)(2)(2)(2)
(1)(1)(2)(2)(3)(3)
(1)(2)(3)(4)(5)(6)


CROSSREFS

Row sums of A322789.
Cf. A007716, A049311, A064573, A279787, A283877, A306017, A316980, A316981, A316983, A319616.
Sequence in context: A007426 A353267 A339336 * A050348 A134637 A078910
Adjacent sequences: A319053 A319054 A319055 * A319057 A319058 A319059


KEYWORD

nonn


AUTHOR

Gus Wiseman, Oct 10 2018


EXTENSIONS

Terms a(12) and beyond from Andrew Howroyd, Feb 03 2022


STATUS

approved



