A303382
Expansion of Product_{n>=1} ((1 + 8*x^n)/(1 - 8*x^n))^(1/8).
Original entry on oeis.org
1, 2, 4, 50, 98, 1830, 4576, 83950, 236500, 4211766, 12903260, 222377926, 723722602, 12136867530, 41382435824, 678060771778, 2400028798290, 38546050682278, 140724756748476, 2220907298526934, 8323586858891766, 129340015891714962, 495838256186203600
Offset: 0
Expansion of Product_{n>=1} ((1 + 2^b*x^n)/(1 - 2^b*x^n))^(1/(2^b)):
A015128 (b=0),
A303346 (b=1),
A303360 (b=2), this sequence (b=3).
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seq(coeff(series(mul(((1+8*x^k)/(1-8*x^k))^(1/8), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018
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nmax = 25; CoefficientList[Series[Product[((1 + 8*x^k)/(1 - 8*x^k))^(1/8), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 23 2018 *)
nmax = 30; CoefficientList[Series[(-7*QPochhammer[-8, x] / (9*QPochhammer[8, x]))^(1/8), {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 23 2018 *)
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N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+8*x^k)/(1-8*x^k))^(1/8)))
A303440
Expansion of Product_{k>=1} ((1 + (2^k*x)^k)/(1 - (2^k*x)^k))^(1/2^k).
Original entry on oeis.org
1, 2, 10, 148, 8502, 2114924, 2151771524, 8800410198536, 144132802083312550, 9445021284412120235340, 2475898969479166225559648172, 2596153381122039693822323043973720, 10889040933791649565507987988056678914620
Offset: 0
A303395
Expansion of Product_{n>=1} ((1 - (8*x)^n)/(1 + (8*x)^n))^(1/8).
Original entry on oeis.org
1, -2, -14, -140, -586, -5628, -44492, -187864, -482906, -17262828, -37958116, 65242328, -2453533124, 21817485480, 113877127592, -2570293967536, 28064994368262, 169252831757492, -188223954450804, 12624245609040632, 54083158292451540, -158891267358816264
Offset: 0
Expansion of Product_{n>=1} ((1 + (2^b*x)^n)/(1 - (2^b)*x^n))^(1/(2^b)):
A002448 (b=0),
A303306 (b=1),
A303394 (b=2), this sequence (b=3).
A303443
Expansion of Product_{k>=1} ((1 + 8^k*x^k)/(1 - 8^k*x^k))^(1/8^k).
Original entry on oeis.org
1, 2, 4, 50, 98, 1830, 7264, 89326, 247252, 4520886, 20225372, 241414342, 786393322, 12744704970, 62688642800, 771140700226, 2635449405522, 40907909552038, 211134761381948, 2451388697035478, 9148627707018230, 143396849321918482, 743716982801639120
Offset: 0
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nmax = 30; CoefficientList[Series[Exp[Sum[((-1)^j - 1) / (j*(1 - 1/(8^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)
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N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+8^k*x^k)/(1-8^k*x^k))^(1/8^k)))
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