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 A241549 #4 May 03 2014 11:31:01
%S A241549 0,0,0,0,0,0,1,1,2,3,5,8,12,17,25,35,48,67,91,122,163,215,283,369,478,
%T A241549 615,786,1004,1270,1604,2014,2521,3139,3902,4824,5954,7314,8970,10957,
%U A241549 13362,16232,19691,23804,28737,34581,41559,49802,59596,71139,84799
%N A241549 Number of partitions p of n such that (number of numbers of the form 5k in p) is a part of p.
%C A241549 Each number in p is counted once, regardless of its multiplicity.
%e A241549 a(6) counts this single partition: 51.
%t A241549 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
%t A241549 Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241549 *)
%t A241549 Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241550 *)
%t A241549 Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241551 *)
%t A241549 Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}] (* A241552 *)
%t A241549 Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}] (* A241553 *)
%Y A241549 Cf. A241550, A241551, A241552, A241553.
%K A241549 nonn,easy
%O A241549 0,9
%A A241549 _Clark Kimberling_, Apr 26 2014