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A282921
Expansion of Product_{k>=1} (1 - x^(7*k))^12/(1 - x^k)^13 in powers of x.
2
1, 13, 104, 637, 3276, 14820, 60697, 229360, 810498, 2705118, 8592857, 26134654, 76476816, 216174700, 592220696, 1576826355, 4090222409, 10357895639, 25653139694, 62235901689, 148108568986, 346176981673, 795569268689, 1799508071426, 4009753651904, 8808973137510
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1 - x^(7*n))^12/(1 - x^n)^13.
a(n) ~ exp(Pi*sqrt(158*n/21)) * sqrt(79) / (4*sqrt(3) * 7^(13/2) * n). - Vaclav Kotesovec, Nov 10 2017
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^12/(1 - x^k)^13, {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))^12/(1 - x^j)^13)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^12/(1 - x^j)^13: 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))^12/(1 - x^j)^13 for j in (1..m))
list(s) # G. C. Greubel, Nov 18 2018
CROSSREFS
Cf. A282919.
Sequence in context: A129762 A283121 A278555 * A023011 A022641 A000590
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved