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 A183088 #21 Nov 21 2013 13:12:28
%S A183088 0,1,3,6,11,19,32,50,77,115,170,244,348,485,674,922,1251,1678,2241,
%T A183088 2959,3892,5076,6592,8497,10915,13930,17719,22417,28267,35474,44395,
%U A183088 55312,68730,85082,105049,129261,158675,194171,237077,288651
%N A183088 Total number of parts that are partition numbers A000041 in all partitions of n.
%H A183088 Alois P. Heinz, <a href="/A183088/b183088.txt">Table of n, a(n) for n = 0..1000</a>
%e A183088 a(5) = 19 because the 7 partitions of 5 are [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and we can see that there are 19 parts that are partition numbers A000041. Note that there are 20 parts but the 4 is not a partition number, so a(5) = 20 - 1 = 19.
%t A183088 A000041 = Table[PartitionsP[n], {n, 0, 45}]; Table[Length[Select[Flatten[IntegerPartitions[n]], MemberQ[A000041, #] &]], {n, 40}] (* _Alonso del Arte_, Aug 05 2011 *)
%Y A183088 Cf. A006128, A037032, A144115.
%K A183088 nonn,less
%O A183088 0,3
%A A183088 _Omar E. Pol_, Aug 05 2011