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 A109708 #17 Mar 20 2017 12:27:02
%S A109708 1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,1,2,1,0,0,1,1,2,2,
%T A109708 1,0,1,1,2,3,3,1,1,1,2,3,4,3,2,1,2,3,5,5,5,2,2,3,5,6,8,5,3,3,5,7,10,9,
%U A109708 7,4,5,7,11,12,12,8,6,7,12,14,17,15,11,8,12,15,20,21,19,13,13,16,22,26,28,23
%N A109708 Number of partitions of n into parts each equal to 6 mod 7.
%H A109708 Vaclav Kotesovec, <a href="/A109708/b109708.txt">Table of n, a(n) for n = 0..10000</a>
%F A109708 G.f.: 1/product(1-x^(6+7j), j=0..infinity). - _Emeric Deutsch_, Apr 14 2006
%F A109708 a(n) ~ Gamma(6/7) * exp(Pi*sqrt(2*n/21)) / (2^(27/14) * 3^(3/7) * 7^(1/14) * Pi^(1/7) * n^(13/14)) * (1 - (39*sqrt(3/14)/(7*Pi) + 13*Pi/(168*sqrt(42))) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F A109708 a(n) = (1/n)*Sum_{k=1..n} A284105(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%e A109708 a(45)=3 because we have 45=27+6+6+6=20+13+6+6=13+13+13+6.
%p A109708 g:=1/product(1-x^(6+7*j),j=0..20): gser:=series(g,x=0,98): seq(coeff(gser,x,n),n=0..95); # _Emeric Deutsch_, Apr 14 2006
%t A109708 nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+6)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%Y A109708 Cf. A284105.
%Y A109708 Cf. similar sequences of number of partitions of n into parts congruent to m-1 mod m: A000009 (m=2), A035386 (m=3), A035462 (m=4), A109700 (m=5), A109702 (m=6), this sequence (m=7).
%K A109708 nonn
%O A109708 0,27
%A A109708 _Erich Friedman_, Aug 07 2005
%E A109708 Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015