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 A325702 #8 Jul 05 2019 18:32:19
%S A325702 1,1,0,0,2,1,2,1,3,3,8,7,10,13,17,19,28,35,38,51,67,81,100,128,157,
%T A325702 195,233,285,348,427,506,613,733,873,1063,1263,1503,1802,2131,2537,
%U A325702 3005,3565,4171,4922,5820,6775,8001,9333,10860,12739,14840,17206,20029,23248
%N A325702 Number of integer partitions of n containing their multiset of multiplicities (as a submultiset).
%C A325702 The Heinz numbers of these partitions are given by A325755.
%e A325702 The partition x = (4,3,1,1,1) has multiplicities (3,1,1), which are a submultiset of x, so x is counted under a(10).
%e A325702 The a(1) = 1 through a(11) = 7 partitions:
%e A325702 (1) (22) (221) (2211) (3211) (4211) (333) (3322) (7211)
%e A325702 (211) (3111) (32111) (5211) (3331) (33221)
%e A325702 (41111) (32211) (6211) (52211)
%e A325702 (42211) (53111)
%e A325702 (43111) (322211)
%e A325702 (322111) (332111)
%e A325702 (421111) (431111)
%e A325702 (511111)
%t A325702 submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap]
%t A325702 Table[Length[Select[IntegerPartitions[n],submultQ[Sort[Length/@Split[#]],#]&]],{n,0,30}]
%Y A325702 Cf. A000041, A181819, A225486, A290689, A290822, A304360, A323014, A324736, A324748, A324753, A324843, A325254, A325755.
%K A325702 nonn
%O A325702 0,5
%A A325702 _Gus Wiseman_, May 18 2019