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A282930
Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.
2
1, 49, 1274, 23275, 334425, 4015011, 41818315, 387605443, 3256150548, 25135003348, 180196297050, 1210028211210, 7663549175191, 46039891115155, 263630633610437, 1444741006154614, 7604013727493190, 38554851707435000, 188824087108333495, 895363849845490543, 4119191297378031000, 18420594133878904635, 80204828814019528689
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1 - x^(7*n))^48/(1 - x^n)^49.
a(n) ~ exp(Pi*sqrt(590*n/21)) * sqrt(295) / (4*sqrt(3) * 7^(49/2) * n). - Vaclav Kotesovec, Nov 10 2017
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^48/(1 - x^k)^49, {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))^48/(1 - x^j)^49)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^48/(1 - x^j)^49: 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))^48/(1 - x^j)^49 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018
CROSSREFS
Cf. A282919.
Sequence in context: A269418 A115999 A228258 * A012238 A036226 A032655
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved