login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)