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A282928 Expansion of Product_{k>=1} (1 - x^(7*k))^40/(1 - x^k)^41 in powers of x. 2
1, 41, 902, 14063, 173635, 1801745, 16300739, 131814181, 969824701, 6579564585, 41587633402, 246925024493, 1386436741480, 7402293438974, 37755020009290, 184685764132377, 869379223328495, 3949788012868677, 17363552010806127 (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))^40/(1 - x^n)^41.

a(n) ~ exp(Pi*sqrt(494*n/21)) * sqrt(247) / (4*sqrt(3) * 7^(41/2) * n). - Vaclav Kotesovec, Nov 10 2017

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^40/(1 - x^k)^41, {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))^40/(1 - x^j)^41)) \\ G. C. Greubel, Nov 18 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^40/(1 - x^j)^41: j in [1..5]]) )); // G. C. Greubel, Nov 18 2018

(Sage) s=(prod((1 - x^(7*j))^40/(1 - x^j)^41 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: A228257 A182359 A090836 * A114529 A300173 A293619

Adjacent sequences:  A282925 A282926 A282927 * A282929 A282930 A282931

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 24 2017

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)