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A282925 Expansion of Product_{k>=1} (1 - x^(7*k))^28/(1 - x^k)^29 in powers of x. 2
1, 29, 464, 5365, 49880, 394632, 2750969, 17296732, 99742368, 534126988, 2681856693, 12722233068, 57373155952, 247218913828, 1022189562610, 4070289420139, 15656921120982, 58336024110584, 211023516790156, 742643172981206, 2547265600634862, 8529351700138885 (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))^28/(1 - x^n)^29.

a(n) ~ exp(Pi*sqrt(350*n/21)) * sqrt(175) / (4*sqrt(3) * 7^(29/2) * n). - Vaclav Kotesovec, Nov 10 2017

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^28/(1 - x^k)^29, {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))^28/(1 - x^j)^29)) \\ G. C. Greubel, Nov 18 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^28/(1 - x^j)^29: j in [1..5]]) )); // G. C. Greubel, Nov 18 2018

(Sage) s=(prod((1 - x^(7*j))^28/(1 - x^j)^29 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: A022593 A078115 A125486 * A022657 A182014 A261540

Adjacent sequences:  A282922 A282923 A282924 * A282926 A282927 A282928

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 24 2017

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)