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A282922
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Expansion of Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17 in powers of x.
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2
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1, 17, 170, 1275, 7905, 42619, 206091, 912459, 3753328, 14500320, 53053498, 185046190, 618555931, 1990227519, 6186291009, 18633598578, 54530992072, 155401842842, 432109571275, 1174385295541, 3124445373406, 8148428799893, 20856618453595, 52451748129498
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17.
a(n) ~ exp(Pi*sqrt(206*n/21)) * sqrt(103) / (4*sqrt(3) * 7^(17/2) * n). - Vaclav Kotesovec, Nov 10 2017
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MATHEMATICA
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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 *)
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PROG
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(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
(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
(Sage)
m = 30
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(m)
s = prod((1 - x^(7*j))^16/(1 - x^j)^17 for j in (1..m))
s.coefficients() # G. C. Greubel, Nov 18 2018
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CROSSREFS
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Cf. A282919.
Sequence in context: A157688 A155658 A121037 * A023015 A022645 A326211
Adjacent sequences: A282919 A282920 A282921 * A282923 A282924 A282925
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Feb 24 2017
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STATUS
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approved
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