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 A301563 #8 Mar 24 2018 19:06:44
%S A301563 1,1,0,1,1,0,1,1,1,2,1,2,2,1,3,2,2,4,3,4,4,4,6,4,6,7,5,9,8,8,11,9,12,
%T A301563 12,12,16,13,17,19,17,23,21,24,27,24,32,30,32,40,35,43,45,44,53,50,59,
%U A301563 62,61,75,70,78,87,83,99,97,105,118,112,133,134,138,159,153
%N A301563 Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+3)).
%C A301563 Number of partitions of n into distinct parts congruent to 1 or 3 mod 5.
%H A301563 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A301563 G.f.: Product_{k>=1} (1 + x^A047219(k)).
%F A301563 a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(21/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e A301563 a(14) = 3 because we have [13, 1], [11, 3] and [8, 6].
%t A301563 nmax = 72; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]
%t A301563 nmax = 72; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^3, x^5], {x, 0, nmax}], x]
%t A301563 nmax = 72; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A301563 Cf. A035372, A047219, A107234, A107236, A203776, A219607, A280454, A281271, A301562, A301564, A301565, A301567, A301568, A301569, A301570.
%K A301563 nonn
%O A301563 0,10
%A A301563 _Ilya Gutkovskiy_, Mar 23 2018