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 A282922 Expansion of Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17 in powers of x. 2
 1, 17, 170, 1275, 7905, 42619, 206091, 912459, 3753328, 14500320, 53053498, 185046190, 618555931, 1990227519, 6186291009, 18633598578, 54530992072, 155401842842, 432109571275, 1174385295541, 3124445373406, 8148428799893, 20856618453595, 52451748129498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA 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 MATHEMATICA 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 *) PROG (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:=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 CROSSREFS Cf. A282919. Sequence in context: A157688 A155658 A121037 * A023015 A022645 A326211 Adjacent sequences: A282919 A282920 A282921 * A282923 A282924 A282925 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 24 2017 STATUS approved

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Last modified March 25 13:31 EDT 2023. Contains 361524 sequences. (Running on oeis4.)