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 A282929 Expansion of Product_{k>=1} (1 - x^(7*k))^44/(1 - x^k)^45 in powers of x. 2
 1, 45, 1080, 18285, 244260, 2733804, 26606745, 230915656, 1819708110, 13198528010, 89041203249, 563420646090, 3366705675744, 19105222953420, 103448715353372, 536621238174195, 2675953974595655, 12866398610335149, 59805282183021050, 269356649381129943, 1177903345233332970, 5010462608512204473, 20765528801742226455 (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))^44/(1 - x^n)^45. a(n) ~ exp(Pi*sqrt(542*n/21)) * sqrt(271) / (4*sqrt(3) * 7^(45/2) * n). - Vaclav Kotesovec, Nov 10 2017 MAPLE N:= 30: gN:= mul((1-x^(7*n))^44/(1-x^n)^45, n=1..N): S:=series(gN, x, N+1): seq(coeff(S, x, n), n=1..N); # Robert Israel, Nov 18 2018 MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^44/(1 - x^k)^45, {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))^44/(1 - x^j)^45)) \\ G. C. Greubel, Nov 18 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^44/(1 - x^j)^45: 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))^44/(1 - x^j)^45 for j in (1..prec)) print(s.coefficients()) # G. C. Greubel, Nov 18 2018 CROSSREFS Cf. A282919. Sequence in context: A163721 A292209 A317895 * A177728 A265615 A320363 Adjacent sequences:  A282926 A282927 A282928 * A282930 A282931 A282932 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 24 2017 STATUS approved

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Last modified June 29 23:00 EDT 2022. Contains 354913 sequences. (Running on oeis4.)