cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A323531 Number of square multiset partitions of integer partitions of n.

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%I A323531 #4 Jan 22 2019 07:45:41
%S A323531 1,1,1,1,2,2,4,5,9,12,18,24,36,48,69,97,139,196,283,402,576,819,1161,
%T A323531 1635,2301,3209,4469,6193,8571,11812,16291,22404,30850,42414,58393,
%U A323531 80305,110578,152091,209308,287686,395352,542413,743603,1017489,1390510,1896482
%N A323531 Number of square multiset partitions of integer partitions of n.
%C A323531 A multiset partition is square if the number of parts is equal to the number of parts in each part.
%e A323531 The a(3) = 1 through a(9) = 12 square multiset partitions:
%e A323531   (3)  (4)       (5)       (6)       (7)       (8)       (9)
%e A323531        (11)(11)  (21)(11)  (21)(21)  (22)(21)  (22)(22)  (32)(22)
%e A323531                            (22)(11)  (31)(21)  (31)(22)  (32)(31)
%e A323531                            (31)(11)  (32)(11)  (31)(31)  (33)(21)
%e A323531                                      (41)(11)  (32)(21)  (41)(22)
%e A323531                                                (33)(11)  (41)(31)
%e A323531                                                (41)(21)  (42)(21)
%e A323531                                                (42)(11)  (43)(11)
%e A323531                                                (51)(11)  (51)(21)
%e A323531                                                          (52)(11)
%e A323531                                                          (61)(11)
%e A323531                                                          (111)(111)(111)
%t A323531 Table[Sum[Length[Union@@(Union[Sort/@Tuples[IntegerPartitions[#,{k}]&/@#]]&/@IntegerPartitions[n,{k}])],{k,Sqrt[n]}],{n,30}]
%Y A323531 Cf. A000219, A001970, A047968, A261049, A279787, A305551, A319066, A323580.
%K A323531 nonn
%O A323531 0,5
%A A323531 _Gus Wiseman_, Jan 21 2019