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 A301564 #7 Mar 24 2018 19:07:23
%S A301564 1,0,1,0,1,0,1,1,0,2,0,2,1,2,2,1,3,1,3,3,2,5,2,6,3,5,6,4,8,5,8,8,7,12,
%T A301564 7,13,11,11,16,11,19,14,19,21,17,27,20,27,28,26,36,28,40,37,38,49,39,
%U A301564 55,49,55,64,55,76,65,78,84,78,100,87,107,109,107,134,116,145
%N A301564 Expansion of Product_{k>=0} (1 + x^(5*k+2))*(1 + x^(5*k+4)).
%C A301564 Number of partitions of n into distinct parts congruent to 2 or 4 mod 5.
%H A301564 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A301564 G.f.: Product_{k>=1} (1 + x^A047211(k)).
%F A301564 a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(29/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e A301564 a(16) = 3 because we have [14, 2], [12, 4] and [9, 7].
%t A301564 nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k + 2)) (1 + x^(5 k + 4)), {k, 0, nmax}], {x, 0, nmax}], x]
%t A301564 nmax = 74; CoefficientList[Series[QPochhammer[-x^2, x^5] QPochhammer[-x^4, x^5], {x, 0, nmax}], x]
%t A301564 nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{2, 4}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A301564 Cf. A035373, A047211, A107235, A107237, A203776, A219607, A281243, A281272, A301562, A301563, A301565, A301567, A301568, A301569, A301570.
%K A301564 nonn
%O A301564 0,10
%A A301564 _Ilya Gutkovskiy_, Mar 23 2018