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.
%I A323774 #19 Nov 30 2024 16:45:57
%S A323774 1,1,3,3,7,3,12,3,16,8,14,3,39,3,16,15,40,3,50,3,54,17,20,3,135,10,22,
%T A323774 25,73,3,129,3,119,21,26,19,273,3,28,23,217,3,203,3,123,74,32,3,590,
%U A323774 12,106,27,154,3,370,23,343,29,38,3,963,3,40,95,450,25,467,3
%N A323774 Number of multiset partitions, whose parts are constant and all have the same sum, of integer partitions of n.
%C A323774 An unlabeled version of A279789.
%H A323774 Antti Karttunen, <a href="/A323774/b323774.txt">Table of n, a(n) for n = 0..20000</a>
%F A323774 a(0) = 1; a(n) = Sum_{d|n} binomial(tau(d) + n/d - 1, n/d), where tau = A000005.
%e A323774 The a(1) = 1 through a(6) = 12 multiset partitions:
%e A323774 (1) (2) (3) (4) (5) (6)
%e A323774 (11) (111) (22) (11111) (33)
%e A323774 (1)(1) (1)(1)(1) (1111) (1)(1)(1)(1)(1) (222)
%e A323774 (2)(2) (3)(3)
%e A323774 (2)(11) (111111)
%e A323774 (11)(11) (3)(111)
%e A323774 (1)(1)(1)(1) (2)(2)(2)
%e A323774 (111)(111)
%e A323774 (2)(2)(11)
%e A323774 (2)(11)(11)
%e A323774 (11)(11)(11)
%e A323774 (1)(1)(1)(1)(1)(1)
%t A323774 Table[Length[Join@@Table[Union[Sort/@Tuples[Select[IntegerPartitions[#],SameQ@@#&]&/@ptn]],{ptn,Select[IntegerPartitions[n],SameQ@@#&]}]],{n,30}]
%o A323774 (PARI) a(n) = if (n==0, 1, sumdiv(n, d, binomial(numdiv(d) + n/d - 1, n/d))); \\ _Michel Marcus_, Jan 28 2019
%Y A323774 Cf. A001970, A006171 (constant parts), A007716, A034729, A047966 (uniform partitions), A047968, A279787, A279789 (twice-partitions version), A305551 (equal part-sums), A306017, A319056, A323766, A323775, A323776.
%K A323774 nonn
%O A323774 0,3
%A A323774 _Gus Wiseman_, Jan 27 2019