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 A301568 #8 Mar 24 2018 19:09:08
%S A301568 1,0,1,0,0,1,0,2,0,1,1,0,3,0,2,2,0,5,0,4,2,1,7,0,7,3,2,10,0,11,4,4,14,
%T A301568 0,17,5,8,19,1,25,6,13,25,2,36,8,21,33,4,50,10,33,43,8,69,12,49,55,14,
%U A301568 93,16,71,70,23,124,20,102,88,37,163,26,142,110,57,212
%N A301568 Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-3)).
%C A301568 Number of partitions of n into distinct parts congruent to 0 or 2 mod 5.
%H A301568 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A301568 G.f.: Product_{k>=1} (1 + x^A047215(k)).
%F A301568 a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(33/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e A301568 a(12) = 3 because we have [12], [10, 2] and [7, 5].
%t A301568 nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A301568 nmax = 74; CoefficientList[Series[x^3 QPochhammer[-1, x^5] QPochhammer[-x^(-3), x^5]/(2 (1 + x) (1 - x + x^2)), {x, 0, nmax}], x]
%t A301568 nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 2}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A301568 Cf. A035368, A036822, A047215, A203776, A219607, A281272, A301562, A301563, A301564, A301565, A301567, A301569, A301570.
%K A301568 nonn
%O A301568 0,8
%A A301568 _Ilya Gutkovskiy_, Mar 23 2018