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 A282921 #32 Sep 08 2022 08:46:18 %S A282921 1,13,104,637,3276,14820,60697,229360,810498,2705118,8592857,26134654, %T A282921 76476816,216174700,592220696,1576826355,4090222409,10357895639, %U A282921 25653139694,62235901689,148108568986,346176981673,795569268689,1799508071426,4009753651904,8808973137510 %N A282921 Expansion of Product_{k>=1} (1 - x^(7*k))^12/(1 - x^k)^13 in powers of x. %H A282921 Seiichi Manyama, <a href="/A282921/b282921.txt">Table of n, a(n) for n = 0..1000</a> %F A282921 G.f.: Product_{n>=1} (1 - x^(7*n))^12/(1 - x^n)^13. %F A282921 a(n) ~ exp(Pi*sqrt(158*n/21)) * sqrt(79) / (4*sqrt(3) * 7^(13/2) * n). - _Vaclav Kotesovec_, Nov 10 2017 %t A282921 nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^12/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *) %o A282921 (PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^12/(1 - x^j)^13)) \\ _G. C. Greubel_, Nov 18 2018 %o A282921 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^12/(1 - x^j)^13: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018 %o A282921 (Sage) %o A282921 m = 30 %o A282921 R = PowerSeriesRing(ZZ, 'x') %o A282921 x = R.gen().O(m) %o A282921 s = prod((1 - x^(7*j))^12/(1 - x^j)^13 for j in (1..m)) %o A282921 list(s) # _G. C. Greubel_, Nov 18 2018 %Y A282921 Cf. A282919. %K A282921 nonn %O A282921 0,2 %A A282921 _Seiichi Manyama_, Feb 24 2017