A282923 Expansion of Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21 in powers of x.

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

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A282920 A282921 A282922 * A282924 A282925 A282926

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved