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 A282927 Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x. 2
 1, 37, 740, 10545, 119510, 1142338, 9548849, 71529474, 488650453, 3084466705, 18173253703, 100751920597, 529029597362, 2645187324766, 12651654794629, 58105915432081, 257102694583806, 1099122519498352, 4551159872375703, 18293134887547452 (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))^36/(1 - x^n)^37. a(n) ~ exp(Pi*sqrt(446*n/21)) * sqrt(223) / (4*sqrt(3) * 7^(37/2) * n). - Vaclav Kotesovec, Nov 10 2017 MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^36/(1 - x^k)^37, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *) PROG (PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^36/(1 - x^j)^37)) \\ G. C. Greubel, Nov 18 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^36/(1 - x^j)^37: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018 (Sage) R = PowerSeriesRing(ZZ, 'x') prec = 30 x = R.gen().O(prec) s = prod((1 - x^(7*j))^36/(1 - x^j)^37 for j in (1..prec)) print(s.coefficients()) # G. C. Greubel, Nov 18 2018 CROSSREFS Cf. A282919. Sequence in context: A162389 A010989 A103195 * A220684 A225971 A258463 Adjacent sequences:  A282924 A282925 A282926 * A282928 A282929 A282930 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 24 2017 STATUS approved

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Last modified August 4 13:22 EDT 2020. Contains 336201 sequences. (Running on oeis4.)