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 A301562 #7 Mar 24 2018 19:06:07
%S A301562 1,1,1,1,0,0,1,2,2,2,1,1,2,3,3,2,2,3,5,6,5,4,4,6,8,8,7,7,9,12,13,11,
%T A301562 10,12,16,19,19,17,18,23,27,27,25,25,30,37,40,38,37,42,50,55,54,52,57,
%U A301562 68,77,78,75,78,90,102,106,104,106,120,138,146,144,145,158
%N A301562 Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+2)).
%C A301562 Number of partitions of n into distinct parts congruent to 1 or 2 mod 5.
%H A301562 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A301562 G.f.: Product_{k>=1} (1 + x^A047216(k)).
%F A301562 a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(17/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e A301562 a(13) = 3 because we have [12, 1], [11, 2] and [7, 6].
%t A301562 nmax = 70; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x]
%t A301562 nmax = 70; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^2, x^5], {x, 0, nmax}], x]
%t A301562 nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 2}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A301562 Cf. A035371, A047216, A107234, A107235, A203776, A219607, A280454, A281272, A301563, A301564, A301565, A301567, A301568, A301569, A301570.
%K A301562 nonn
%O A301562 0,8
%A A301562 _Ilya Gutkovskiy_, Mar 23 2018