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 A109705 #16 Mar 28 2017 14:48:19
%S A109705 1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,1,1,1,2,1,1,2,2,1,2,3,1,2,4,2,2,4,
%T A109705 4,2,4,5,3,4,6,5,4,6,7,5,6,8,8,6,9,11,7,9,13,10,9,14,14,10,15,17,14,
%U A109705 15,19,19,16,20,24,20,21,27,27,22,29,33,27,30,38,35,32,41,44,37,43,51,47,45
%N A109705 Number of partitions of n into parts each equal to 3 mod 7.
%H A109705 Vaclav Kotesovec, <a href="/A109705/b109705.txt">Table of n, a(n) for n = 0..10000</a>
%F A109705 G.f.: 1/product(1-x^(3+7j), j=0..infinity). - _Emeric Deutsch_, Apr 14 2006
%F A109705 a(n) ~ Gamma(3/7) * exp(Pi*sqrt(2*n/21)) / (2^(12/7) * 3^(3/14) * 7^(2/7) * Pi^(4/7) * n^(5/7)) * (1 + (23*Pi/(168*sqrt(42)) - 15*sqrt(3/14)/(7*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F A109705 a(n) = (1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 28 2017
%e A109705 a(20)=2 because we have 20=17+3=10+10.
%p A109705 g:=1/product(1-x^(3+7*j),j=0..20): gser:=series(g,x=0,90): seq(coeff(gser,x,n),n=0..87); # _Emeric Deutsch_, Apr 14 2006
%t A109705 nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+3)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%K A109705 nonn
%O A109705 0,21
%A A109705 _Erich Friedman_, Aug 07 2005
%E A109705 Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015