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 A035627 #14 Aug 16 2020 17:06:50
%S A035627 0,0,0,0,0,1,1,1,1,1,4,4,4,4,4,10,11,11,11,11,22,25,26,26,26,44,51,54,
%T A035627 55,55,84,98,105,108,109,153,178,193,200,203,270,313,341,356,363,462,
%U A035627 532,582,611,626,771,883,968,1021,1050,1259,1431,1571,1663,1717,2017
%N A035627 Number of partitions of n into parts 5k and 5k+1 with at least one part of each type.
%H A035627 Robert Price, <a href="/A035627/b035627.txt">Table of n, a(n) for n = 1..1000</a>
%F A035627 G.f.: (-1 + 1/Product_{k>=1} (1 - x^(5 k)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 1))). - _Robert Price_, Aug 16 2020
%t A035627 nmax = 61; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 1;
%t A035627 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035627 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035627 nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 06 2020 *)
%Y A035627 Cf. A035441-A035468, A035618-A035626, A035628-A035699.
%K A035627 nonn
%O A035627 1,11
%A A035627 _Olivier Gérard_