A282927 Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x.

1, 37, 740, 10545, 119510, 1142338, 9548849, 71529474, 488650453, 3084466705, 18173253703, 100751920597, 529029597362, 2645187324766, 12651654794629, 58105915432081, 257102694583806, 1099122519498352, 4551159872375703, 18293134887547452

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))^36/(1 - x^n)^37.

a(n) ~ exp(Pi*sqrt(446*n/21)) * sqrt(223) / (4*sqrt(3) * 7^(37/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^36/(1 - x^k)^37, {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))^36/(1 - x^j)^37)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^36/(1 - x^j)^37: 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))^36/(1 - x^j)^37 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A162389 A010989 A103195 * A220684 A225971 A258463

Adjacent sequences: A282924 A282925 A282926 * A282928 A282929 A282930

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved