login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282927 Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x. 2
1, 37, 740, 10545, 119510, 1142338, 9548849, 71529474, 488650453, 3084466705, 18173253703, 100751920597, 529029597362, 2645187324766, 12651654794629, 58105915432081, 257102694583806, 1099122519498352, 4551159872375703, 18293134887547452 (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))^36/(1 - x^n)^37.

a(n) ~ exp(Pi*sqrt(446*n/21)) * sqrt(223) / (4*sqrt(3) * 7^(37/2) * n). - Vaclav Kotesovec, Nov 10 2017

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^36/(1 - x^k)^37, {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))^36/(1 - x^j)^37)) \\ G. C. Greubel, Nov 18 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^36/(1 - x^j)^37: 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))^36/(1 - x^j)^37 for j in (1..prec))

print(s.coefficients()) # G. C. Greubel, Nov 18 2018

CROSSREFS

Cf. A282919.

Sequence in context: A162389 A010989 A103195 * A220684 A225971 A258463

Adjacent sequences:  A282924 A282925 A282926 * A282928 A282929 A282930

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 13:22 EDT 2020. Contains 336201 sequences. (Running on oeis4.)