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A282926 Expansion of Product_{k>=1} (1 - x^(7*k))^32/(1 - x^k)^33 in powers of x. 2
1, 33, 594, 7667, 79101, 691119, 5299019, 36518791, 230122266, 1343028082, 7331536586, 37731144564, 184232285897, 857974579385, 3827695162667, 16420097827188, 67948512704413, 271990545250303, 1055719283332541, 3981884465793740, 14621550982740229 (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))^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

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Last modified January 17 20:06 EST 2022. Contains 350410 sequences. (Running on oeis4.)