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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<x>:=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.)