A282922 Expansion of Product_{n>=1} (1 - x^(7*n))^16/(1 - x^n)^17 in powers of x.

1, 17, 170, 1275, 7905, 42619, 206091, 912459, 3753328, 14500320, 53053498, 185046190, 618555931, 1990227519, 6186291009, 18633598578, 54530992072, 155401842842, 432109571275, 1174385295541, 3124445373406, 8148428799893, 20856618453595, 52451748129498

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))^16/(1 - x^n)^17.

a(n) ~ exp(Pi*sqrt(206*n/21)) * sqrt(103) / (4*sqrt(3) * 7^(17/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^16/(1 - x^k)^17, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(prod(j=1, 30, (1 - x^(7*j))^16/(1 - x^j)^17)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^16/(1 - x^j)^17: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018
(Sage)
m = 30
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(m)
s = prod((1 - x^(7*j))^16/(1 - x^j)^17 for j in (1..m))
s.coefficients() # G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A157688 A155658 A121037 * A023015 A022645 A326211

Adjacent sequences: A282919 A282920 A282921 * A282923 A282924 A282925

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved