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A282927
Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x.
2
1, 37, 740, 10545, 119510, 1142338, 9548849, 71529474, 488650453, 3084466705, 18173253703, 100751920597, 529029597362, 2645187324766, 12651654794629, 58105915432081, 257102694583806, 1099122519498352, 4551159872375703, 18293134887547452
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved