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 A318029 #5 Aug 18 2018 04:14:23
%S A318029 0,0,0,0,0,1,1,2,2,4,4,6,7,9,11,14,16,20,24,28,34,40,47,55,65,75,88,
%T A318029 102,118,136,158,180,208,238,272,311,355,403,459,521,590,668,756,852,
%U A318029 962,1084,1218,1370,1538,1724,1932,2163,2417,2701,3015,3361,3745,4170,4636,5154,5724
%N A318029 Expansion of Sum_{k>=2} x^(k*(k+3)/2) / Product_{j=1..k} (1 - x^j).
%C A318029 Number of partitions of n into at least two distinct parts >= 2.
%H A318029 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A318029 G.f.: x - 1/(1 - x) + Product_{k>=2} (1 + x^k).
%F A318029 a(n) = A025147(n) - 1 for n > 1.
%e A318029 a(9) = 4 because we have [7, 2], [6, 3], [5, 4] and [4, 3, 2].
%t A318029 nmax = 60; CoefficientList[Series[Sum[x^(k (k + 3)/2)/Product[(1 - x^j), {j, 1, k}], {k, 2, nmax}], {x, 0, nmax}], x]
%t A318029 nmax = 60; CoefficientList[Series[x - 1/(1 - x) + 1/((1 + x) QPochhammer[x, x^2]), {x, 0, nmax}], x]
%t A318029 Join[{0, 0}, Table[-1 + Sum[(-1)^(n - k) PartitionsQ[k], {k, 0, n}], {n, 2, 60}]]
%Y A318029 Cf. A000009, A025147, A083751, A096765, A111133.
%K A318029 nonn
%O A318029 0,8
%A A318029 _Ilya Gutkovskiy_, Aug 13 2018