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 A238742 #7 Mar 12 2014 10:25:40
%S A238742 0,0,1,5,13,31,59,109,180,301,461,712,1051,1547,2200,3138,4349,6036,
%T A238742 8211,11146,14901,19908,26232,34513,44953,58412,75244,96752,123448,
%U A238742 157201,198931,251155
%N A238742 Number of partitions p of 2n+1 such that n - (number of parts of p) is a part of p.
%H A238742 Giovanni Resta, <a href="/A238742/b238742.txt">Table of n, a(n) for n = 1..1000</a>
%e A238742 a(4) counts these partitions of 9: 72, 711, 621, 531, 441.
%t A238742 z = 30; g[n_] := IntegerPartitions[n]; m[p_, t_] := MemberQ[p, t];
%t A238742 Table[Count[g[2 n], p_ /; m[p, n - Length[p]]], {n, z}] (*A238607*)
%t A238742 Table[Count[g[2 n - 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238641*)
%t A238742 Table[Count[g[2 n + 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238742*)
%t A238742 p[n_, k_] := p[n, k] = If[k == 1 || n == k, 1, If[k > n, 0, p[n-1, k-1] + p[n-k, k]]]; q[n_, k_, e_] := q[n, k, e] = If[n-e < k-1 , 0, If[k == 1, If[n == e, 1, 0], p[n-e, k-1]]]; a[n_] := Sum[q[2*n+1, u, n-u], {u, n-1}]; Array[a, 100] (* _Giovanni Resta_, Mar 12 2014 *)
%Y A238742 Cf. A238640, A238741.
%K A238742 nonn,easy
%O A238742 1,4
%A A238742 _Clark Kimberling_, Mar 04 2014