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 A282921 Expansion of Product_{k>=1} (1 - x^(7*k))^12/(1 - x^k)^13 in powers of x. 2
 1, 13, 104, 637, 3276, 14820, 60697, 229360, 810498, 2705118, 8592857, 26134654, 76476816, 216174700, 592220696, 1576826355, 4090222409, 10357895639, 25653139694, 62235901689, 148108568986, 346176981673, 795569268689, 1799508071426, 4009753651904, 8808973137510 (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))^12/(1 - x^n)^13. a(n) ~ exp(Pi*sqrt(158*n/21)) * sqrt(79) / (4*sqrt(3) * 7^(13/2) * n). - Vaclav Kotesovec, Nov 10 2017 MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^12/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *) PROG (PARI) x='x+O('x^30); Vec(prod(j=1, 5, (1 - x^(7*j))^12/(1 - x^j)^13)) \\ G. C. Greubel, Nov 18 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^12/(1 - x^j)^13: j in [1..5]]) )); // G. C. Greubel, Nov 18 2018 (Sage) s=(prod((1 - x^(7*j))^12/(1 - x^j)^13 for j in (1..5))).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 18 2018 CROSSREFS Cf. A282919. Sequence in context: A129762 A283121 A278555 * A023011 A022641 A000590 Adjacent sequences:  A282918 A282919 A282920 * A282922 A282923 A282924 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 24 2017 STATUS approved

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Last modified January 16 04:52 EST 2019. Contains 319187 sequences. (Running on oeis4.)