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 A282920 #33 Sep 08 2022 08:46:18 %S A282920 1,9,54,255,1035,3753,12483,38701,113193,315013,839802,2155905, %T A282920 5352252,12894426,30233558,69160869,154677325,338822547,728084435, %U A282920 1536931932,3190959918,6523084815,13142291319,26118847655,51244059231,99322878506,190306301025 %N A282920 Expansion of Product_{k>=1} (1 - x^(7*k))^8/(1 - x^k)^9 in powers of x. %H A282920 Seiichi Manyama, <a href="/A282920/b282920.txt">Table of n, a(n) for n = 0..1000</a> %F A282920 G.f.: Product_{n>=1} (1 - x^(7*n))^8/(1 - x^n)^9. %F A282920 a(n) ~ exp(Pi*sqrt(110*n/21)) * sqrt(55) / (4*sqrt(3) * 7^(9/2) * n). - _Vaclav Kotesovec_, Nov 10 2017 %t A282920 nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^8 /(1 - x^k)^9, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *) %o A282920 (PARI) my(N=30,x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^8/(1 - x^j)^9)) \\ _G. C. Greubel_, Nov 18 2018 %o A282920 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^8/(1 - x^j)^9: j in [1..m+2]]) )); // _G. C. Greubel_, Nov 18 2018 %o A282920 (Sage) %o A282920 R = PowerSeriesRing(ZZ, 'x') %o A282920 prec = 30 %o A282920 x = R.gen().O(prec) %o A282920 s = prod((1 - x^(7*j))^8/(1 - x^j)^9 for j in (1..prec)) %o A282920 print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018 %Y A282920 Cf. A282919. %K A282920 nonn %O A282920 0,2 %A A282920 _Seiichi Manyama_, Feb 24 2017