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 A241132 #8 Mar 15 2024 21:31:27 %S A241132 0,0,0,0,0,0,1,0,1,1,4,2,5,6,10,16,17,23,32,42,53,79,88,117,146,189, %T A241132 230,298,374,452,562,688,842,1036,1256,1520,1876,2225,2688,3226,3875, %U A241132 4608,5528,6553,7799,9272,10936,12903,15239,17919,21038,24714,28922,33819 %N A241132 Number of partitions p of n such that (maximal multiplicity over the parts of p) = (number of numbers in p having multiplicity > 1). %H A241132 Alois P. Heinz, <a href="/A241132/b241132.txt">Table of n, a(n) for n = 0..1000</a> %e A241132 a(10) counts these 4 partitions: 4411, 42211, 3322, 33211. %t A241132 z = 30; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; %t A241132 m[p_] := Max[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; m[p] == e[p]], {n, 0, z}] %Y A241132 Cf. A241090, A241131. %K A241132 nonn,easy %O A241132 0,11 %A A241132 _Clark Kimberling_, Apr 24 2014