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 A277090 #18 Mar 20 2017 04:20:20
%S A277090 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,4,4,4,4,4,4,4,5,6,7,7,7,7,7,7,8,
%T A277090 10,11,12,12,12,12,12,13,15,17,18,19,19,19,19,20,23,26,28,29,30,30,30,
%U A277090 31,34,38,41,43,44,45,45,46,50,55,60,63,65,66,67,68,72,79,85,90,93,95,96,98,103,111,120,127,132,135,137,139,145
%N A277090 Expansion of Product_{k>=0} 1/(1 - x^(8*k+1)).
%C A277090 Number of partitions of n into parts congruent to 1 mod 8.
%C A277090 More generally, the ordinary generating function for the number of partitions of n into parts congruent to 1 mod m (for m>0) is Product_{k>=0} 1/(1 - x^(m*k+1)).
%H A277090 Seiichi Manyama, <a href="/A277090/b277090.txt">Table of n, a(n) for n = 0..10000</a>
%H A277090 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015.
%H A277090 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A277090 G.f.: Product_{k>=0} 1/(1 - x^(8*k+1)).
%F A277090 a(n) ~ exp((Pi*sqrt(n))/(2*sqrt(3)))*Gamma(1/8)/(4*3^(1/16)*(2*Pi)^(7/8)*n^(9/16)).
%F A277090 a(n) = (1/n)*Sum_{k=1..n} A284100(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%e A277090 a(10) = 2, because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t A277090 CoefficientList[Series[QPochhammer[x, x^8]^(-1), {x, 0, 90}], x]
%Y A277090 Cf. A017077, A284100.
%Y A277090 Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), A035451 (m=4), A109697 (m=5), A109701 (m=6), A109703 (m=7).
%K A277090 nonn
%O A277090 0,10
%A A277090 _Ilya Gutkovskiy_, Sep 29 2016