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 A235130 #6 Feb 07 2014 11:34:15
%S A235130 1,1,2,2,2,3,3,3,3,5,5,5,5,5,7,7,8,6,7,7,11,11,11,11,11,10,11,15,15,
%T A235130 17,15,14,13,15,15,22,22,23,23,21,22,19,20,22,30,30,33,30,33,25,29,25,
%U A235130 29,30,42,42,45,44,43,41,42,36,36,39,42,56,56,62,58,60
%N A235130 Triangular array: t(n,k) = number of partitions of n that include a partition of k.
%H A235130 Clark Kimberling, <a href="/A235130/b235130.txt">Table of n, a(n) for n = 1..300</a>
%F A235130 t(n,1) = A000041(n-1) for n>=0; t(n,n) = A000041(n) for n >= 1.
%e A235130 The eleven partitions of 6 include the following six, written as multisets: {1,1,1,1,1,1}, {1,1,1,1,2}, {1,1,2,2}, {1,1,1,3}, {1,2,3}, {3,3}; each has a sub-multiset of which the sum of terms is 3. None of the remaining five partitions of 6 has this property, so t(6,3) = 6. First 7 rows:
%e A235130 1
%e A235130 1 ... 2
%e A235130 2 ... 2 ... 3
%e A235130 3 ... 3 ... 3 ... 5
%e A235130 5 ... 5 ... 5 ... 5 ... 7
%e A235130 7 ... 8 ... 6 ... 7 ... 7 ... 11
%e A235130 11 .. 11 .. 11 .. 11 .. 10 .. 11 .. 15
%t A235130 p[n_] := p[n] = IntegerPartitions[n]; t = Table[Length[Cases[p[n], Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p[k]]]]], {n, 15}, {k, n}]; u = Flatten[t] (* 235130 *)
%t A235130 TableForm[t] (* _Peter J. C. Moses_, Jan 04 2014 *)
%Y A235130 Cf. A000041.
%K A235130 nonn,tabl
%O A235130 1,3
%A A235130 _Clark Kimberling_, Jan 03 2014