A282922 - OEIS

%I #25 Sep 08 2022 08:46:18

%S 1,17,170,1275,7905,42619,206091,912459,3753328,14500320,53053498,

%T 185046190,618555931,1990227519,6186291009,18633598578,54530992072,

%U 155401842842,432109571275,1174385295541,3124445373406,8148428799893,20856618453595,52451748129498

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

%H Seiichi Manyama, <a href="/A282922/b282922.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17.

%F a(n) ~ exp(Pi*sqrt(206*n/21)) * sqrt(103) / (4*sqrt(3) * 7^(17/2) * n). - _Vaclav Kotesovec_, Nov 10 2017

%t 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 (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 (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 (Sage)

%o m = 30

%o R = PowerSeriesRing(ZZ, 'x')

%o x = R.gen().O(m)

%o s = prod((1 - x^(7*j))^16/(1 - x^j)^17 for j in (1..m))

%o s.coefficients() # _G. C. Greubel_, Nov 18 2018

%Y Cf. A282919.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 24 2017