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A282923
Expansion of Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21 in powers of x.
2
1, 21, 252, 2233, 16170, 100926, 560945, 2837398, 13265679, 57989435, 239125579, 936702879, 3505361650, 12590400326, 43572202835, 145770820937, 472764167939, 1490002933265, 4573182416677, 13694526423445, 40076281579264, 114782535792335, 322167257486123, 887188897987819, 2399619923361150, 6380874322337452, 16695968482412345
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21.
a(n) ~ exp(Pi*sqrt(254*n/21)) * sqrt(127) / (4*sqrt(3) * 7^(21/2) * n). - Vaclav Kotesovec, Nov 10 2017
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^20/(1 - x^k)^21, {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))^20/(1 - x^j)^21)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^20/(1 - x^j)^21: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^20/(1 - x^j)^21 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018
CROSSREFS
Cf. A282919.
Sequence in context: A165095 A165099 A165108 * A023019 A036220 A022649
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved