A282926 Expansion of Product_{k>=1} (1 - x^(7*k))^32/(1 - x^k)^33 in powers of x.

1, 33, 594, 7667, 79101, 691119, 5299019, 36518791, 230122266, 1343028082, 7331536586, 37731144564, 184232285897, 857974579385, 3827695162667, 16420097827188, 67948512704413, 271990545250303, 1055719283332541, 3981884465793740, 14621550982740229

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))^32/(1 - x^n)^33.

a(n) ~ exp(Pi*sqrt(398*n/21)) * sqrt(199) / (4*sqrt(3) * 7^(33/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^32/(1 - x^k)^33, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Prog

(PARI) my(m=30, x='x+O('x^m)); Vec(prod(j=1, m, (1 - x^(7*j))^32/(1 - x^j)^33)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^32/(1 - x^j)^33: j in [1..m]]) )); // G. C. Greubel, Nov 18 2018
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^32/(1 - x^j)^33 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A010985 A228256 A197361 * A172362 A080597 A076684

Adjacent sequences: A282923 A282924 A282925 * A282927 A282928 A282929

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved