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 A282927 #34 Sep 08 2022 08:46:18 %S A282927 1,37,740,10545,119510,1142338,9548849,71529474,488650453,3084466705, %T A282927 18173253703,100751920597,529029597362,2645187324766,12651654794629, %U A282927 58105915432081,257102694583806,1099122519498352,4551159872375703,18293134887547452 %N A282927 Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x. %H A282927 Seiichi Manyama, <a href="/A282927/b282927.txt">Table of n, a(n) for n = 0..1000</a> %F A282927 G.f.: Product_{n>=1} (1 - x^(7*n))^36/(1 - x^n)^37. %F A282927 a(n) ~ exp(Pi*sqrt(446*n/21)) * sqrt(223) / (4*sqrt(3) * 7^(37/2) * n). - _Vaclav Kotesovec_, Nov 10 2017 %t A282927 nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^36/(1 - x^k)^37, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *) %o A282927 (PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^36/(1 - x^j)^37)) \\ _G. C. Greubel_, Nov 18 2018 %o A282927 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^36/(1 - x^j)^37: j in [1..m+2]]) )); // _G. C. Greubel_, Nov 18 2018 %o A282927 (Sage) %o A282927 R = PowerSeriesRing(ZZ, 'x') %o A282927 prec = 30 %o A282927 x = R.gen().O(prec) %o A282927 s = prod((1 - x^(7*j))^36/(1 - x^j)^37 for j in (1..prec)) %o A282927 print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018 %Y A282927 Cf. A282919. %K A282927 nonn %O A282927 0,2 %A A282927 _Seiichi Manyama_, Feb 24 2017