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A282922 Expansion of Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17 in powers of x.

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%I A282922 #25 Sep 08 2022 08:46:18
%S A282922 1,17,170,1275,7905,42619,206091,912459,3753328,14500320,53053498,
%T A282922 185046190,618555931,1990227519,6186291009,18633598578,54530992072,
%U A282922 155401842842,432109571275,1174385295541,3124445373406,8148428799893,20856618453595,52451748129498
%N A282922 Expansion of Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17 in powers of x.
%H A282922 Seiichi Manyama, <a href="/A282922/b282922.txt">Table of n, a(n) for n = 0..1000</a>
%F A282922 G.f.: Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17.
%F A282922 a(n) ~ exp(Pi*sqrt(206*n/21)) * sqrt(103) / (4*sqrt(3) * 7^(17/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t A282922 nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^16/(1 - x^k)^17, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o A282922 (PARI) my(x='x+O('x^30)); Vec(prod(j=1, 30, (1 - x^(7*j))^16/(1 - x^j)^17)) \\ _G. C. Greubel_, Nov 18 2018
%o A282922 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^16/(1 - x^j)^17: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018
%o A282922 (Sage)
%o A282922 m = 30
%o A282922 R = PowerSeriesRing(ZZ, 'x')
%o A282922 x = R.gen().O(m)
%o A282922 s = prod((1 - x^(7*j))^16/(1 - x^j)^17 for j in (1..m))
%o A282922 s.coefficients() # _G. C. Greubel_, Nov 18 2018
%Y A282922 Cf. A282919.
%K A282922 nonn
%O A282922 0,2
%A A282922 _Seiichi Manyama_, Feb 24 2017