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 A325766 #6 May 21 2019 22:05:34
%S A325766 1,1,0,0,1,1,1,1,1,1,1,3,1,5,4,5,4,6,7,8,6,12,11,19,16,22,22,25,32,38,
%T A325766 45,45,51,53,71,69,85,92,118,125,147,149,184,187,230,254,290,317,372,
%U A325766 397,449,502,544,616,680,758,841,930,1042,1151,1262
%N A325766 Number of integer partitions of n covering an initial interval of positive integers and containing their own multiset of multiplicities (as a submultiset).
%C A325766 The Heinz numbers of these partitions are given by A325767.
%e A325766 The initial terms count the following partitions:
%e A325766 1: (1)
%e A325766 4: (2,1,1)
%e A325766 5: (2,2,1)
%e A325766 6: (2,2,1,1)
%e A325766 7: (3,2,1,1)
%e A325766 8: (3,2,1,1,1)
%e A325766 9: (3,2,2,1,1)
%e A325766 10: (3,2,2,1,1,1)
%e A325766 11: (3,3,2,2,1)
%e A325766 11: (3,3,2,1,1,1)
%e A325766 11: (3,2,2,2,1,1)
%e A325766 12: (4,3,2,1,1,1)
%e A325766 13: (4,3,2,2,1,1)
%e A325766 13: (4,3,2,1,1,1,1)
%e A325766 13: (3,3,3,2,1,1)
%e A325766 13: (3,3,2,2,2,1)
%e A325766 13: (3,3,2,2,1,1,1)
%e A325766 14: (4,3,2,2,1,1,1)
%e A325766 14: (3,3,3,2,2,1)
%e A325766 14: (3,3,3,2,1,1,1)
%e A325766 14: (3,3,2,2,2,1,1)
%t A325766 submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap]
%t A325766 Table[Length[Select[IntegerPartitions[n],Range[Length[Union[#]]]==Union[#]&&submultQ[Sort[Length/@Split[#]],Sort[#]]&]],{n,0,30}]
%Y A325766 Cf. A000009 (partitions covering an initial interval), A055932, A114639, A114640, A290689, A324753, A325702, A325706, A325707, A325708, A325767.
%K A325766 nonn
%O A325766 0,12
%A A325766 _Gus Wiseman_, May 19 2019