A282920 Expansion of Product_{k>=1} (1 - x^(7*k))^8/(1 - x^k)^9 in powers of x.

1, 9, 54, 255, 1035, 3753, 12483, 38701, 113193, 315013, 839802, 2155905, 5352252, 12894426, 30233558, 69160869, 154677325, 338822547, 728084435, 1536931932, 3190959918, 6523084815, 13142291319, 26118847655, 51244059231, 99322878506, 190306301025

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))^8/(1 - x^n)^9.

a(n) ~ exp(Pi*sqrt(110*n/21)) * sqrt(55) / (4*sqrt(3) * 7^(9/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^8 /(1 - x^k)^9, {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))^8/(1 - x^j)^9)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^8/(1 - x^j)^9: 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))^8/(1 - x^j)^9 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A289254 A059597 A327387 * A023008 A079817 A169796

Adjacent sequences: A282917 A282918 A282919 * A282921 A282922 A282923

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved