A282930
Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.
Original entry on oeis.org
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
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m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^48/(1 - x^j)^49: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018
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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 *)
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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
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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
A282931
Expansion of Product_{k>=1} (1 - x^(7*k))^52/(1 - x^k)^53 in powers of x.
Original entry on oeis.org
1, 53, 1484, 29097, 447426, 5734918, 63638001, 627260142, 5594403499, 45779730871, 347453597091, 2466970932027, 16501339314082, 104588498225862, 631215364345159, 3642533720923593, 20170341090888205, 107511123136305075, 553099301324196585
Offset: 0
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m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^52/(1 - x^j)^53: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018
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nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^52/(1 - x^k)^53, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
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my(N=30,x='x+O('x^N)); Vec(prod(j=1,N, (1 - x^(7*j))^52/(1 - x^j)^53)) \\ G. C. Greubel, Nov 18 2018
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R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^52/(1 - x^j)^53 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018
A282932
Expansion of Product_{k>=1} (1 - x^(7*k))^56/(1 - x^k)^57 in powers of x.
Original entry on oeis.org
1, 57, 1710, 35815, 586815, 7997157, 94175267, 983458849, 9279004863, 80218101555, 642408637594, 4807304399931, 33855173217278, 225702273908048, 1431470152072364, 8673471170235715, 50389686887219910, 281575909008910196, 1517580284619183809
Offset: 0
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m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^56/(1 - x^j)^57: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018
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nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^56/(1 - x^k)^57, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
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my(N=30,x='x+O('x^N)); Vec(prod(j=1,N, (1 - x^(7*j))^56/(1 - x^j)^57)) \\ G. C. Greubel, Nov 18 2018
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R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^56/(1 - x^j)^57 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018
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