A303360
Expansion of Product_{n>=1} ((1 + 4*x^n)/(1 - 4*x^n))^(1/4).
Original entry on oeis.org
1, 2, 4, 18, 34, 166, 384, 1902, 4756, 24022, 64284, 321542, 899658, 4455690, 12888944, 63185250, 187513426, 910880550, 2759413788, 13295839638, 40967821494, 195979968882, 612569599440, 2911592648458, 9213101043936, 43538337410474, 139246245625364
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), this sequence (b=2).
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seq(coeff(series(mul(((1+4*x^k)/(1-4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n = 0..35); # Muniru A Asiru, Apr 22 2018
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nmax = 30; CoefficientList[Series[Product[((1 + 4*x^k)/(1 - 4*x^k))^(1/4), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)
nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/4), {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+4*x^k)/(1-4*x^k))^(1/4)))
A303390
Expansion of Product_{k>=1} (1 + 3*x^k)/(1 - 3*x^k).
Original entry on oeis.org
1, 6, 24, 96, 330, 1104, 3552, 11184, 34584, 105990, 322224, 975264, 2942016, 8857680, 26631312, 80005632, 240219114, 721036320, 2163789816, 6492625152, 19480105392, 58444390176, 175340344416, 526034008752, 1578124753152, 4734415061142, 14203316252400
Offset: 0
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nmax = 30; CoefficientList[Series[Product[(1+3*x^k)/(1-3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
A303402
Expansion of Product_{k>=1} (1 - 4*x^k)/(1 + 4*x^k).
Original entry on oeis.org
1, -8, 24, -72, 344, -1416, 5400, -21576, 87000, -348296, 1390872, -5560776, 22253784, -89025672, 356055960, -1424186568, 5696931032, -22787865096, 91150729368, -364602357960, 1458412314456, -5833651510536, 23334594559128, -93338369011272, 373353522099288
Offset: 0
Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k):
A002448 (b=1),
A303397 (b=2),
A303398 (b=3), this sequence (b=4).
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nmax = 30; CoefficientList[Series[Product[(1 - 4*x^k)/(1 + 4*x^k), {k, 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, (1-4*x^k)/(1+4*x^k)))
A303392
Expansion of Product_{k>=1} ((1 + 4*x^k) / (1 - 4*x^k))^(1/2).
Original entry on oeis.org
1, 4, 12, 52, 156, 612, 2028, 7892, 27324, 107396, 384844, 1520436, 5566876, 22069796, 81990252, 325707348, 1222582268, 4862950020, 18395472460, 73233825524, 278700724764, 1110232691108, 4245596648876, 16920914168148, 64963831455996, 259012955299396
Offset: 0
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nmax = 30; CoefficientList[Series[Product[((1+4*x^k)/(1-4*x^k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/2), {x, 0, nmax}], x]
Showing 1-4 of 4 results.