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 A261733 #12 Sep 01 2015 04:21:46
%S A261733 1,-1,0,-1,1,-1,1,-1,2,-1,1,-2,2,-2,2,-3,4,-3,4,-5,5,-6,6,-7,8,-8,9,
%T A261733 -9,10,-12,11,-13,15,-16,17,-18,22,-23,23,-27,30,-31,32,-35,40,-40,42,
%U A261733 -48,51,-54,57,-63,69,-71,78,-85,90,-97,102,-110,118,-124,133
%N A261733 Expansion of Product_{k>=1} (1 + x^(9*k))/(1 + x^k).
%C A261733 In general, if m > 1 and g.f. = Product_{k>=1} (1 + x^(m*k))/(1 + x^k), then a(n) ~ (-1)^n * exp(Pi*sqrt((m+2)*n/(6*m))) * (m+2)^(1/4) / (4 * (6*m)^(1/4) * n^(3/4)) if m is even and a(n) ~ (-1)^n * exp(Pi*sqrt((m-1)*n/(6*m))) * (m-1)^(1/4) / (2^(3/2) * (6*m)^(1/4) * n^(3/4)) if m is odd.
%H A261733 Alois P. Heinz, <a href="/A261733/b261733.txt">Table of n, a(n) for n = 0..10000</a>
%F A261733 a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/3)/3) / (2 * 3^(3/4) * n^(3/4)).
%p A261733 with(numtheory):
%p A261733 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*[0, -1, 0,
%p A261733 -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1]
%p A261733 [1+irem(d, 18)], d=divisors(j))*a(n-j), j=1..n)/n)
%p A261733 end:
%p A261733 seq(a(n), n=0..80); # _Alois P. Heinz_, Sep 01 2015
%t A261733 nmax = 100; CoefficientList[Series[Product[(1 + x^(9*k))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A261733 Cf. A081360 (m=2), A109389 (m=3), A261734 (m=4), A133563 (m=5), A261736 (m=6), A113297 (m=7), A261735 (m=8), A145707 (m=10).
%K A261733 sign
%O A261733 0,9
%A A261733 _Vaclav Kotesovec_, Aug 30 2015