A282925 Expansion of Product_{k>=1} (1 - x^(7*k))^28/(1 - x^k)^29 in powers of x.

1, 29, 464, 5365, 49880, 394632, 2750969, 17296732, 99742368, 534126988, 2681856693, 12722233068, 57373155952, 247218913828, 1022189562610, 4070289420139, 15656921120982, 58336024110584, 211023516790156, 742643172981206, 2547265600634862, 8529351700138885

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))^28/(1 - x^n)^29.

a(n) ~ exp(Pi*sqrt(350*n/21)) * sqrt(175) / (4*sqrt(3) * 7^(29/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^28/(1 - x^k)^29, {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))^28/(1 - x^j)^29)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^28/(1 - x^j)^29: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^28/(1 - x^j)^29 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A022593 A078115 A125486 * A022657 A182014 A261540

Adjacent sequences: A282922 A282923 A282924 * A282926 A282927 A282928

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved