A303438 -id:A303438 - cp's OEIS frontend

A303439 Expansion of Product_{k>=1} ((1 - 2^kx^k)/(1 + 2^kx^k))^(1/2^k).

1, -2, 0, -2, 6, -6, 4, -6, 48, -118, 96, -78, 470, -810, 396, -3050, 11062, -12678, 7072, -21454, 80034, -201490, 218940, -200658, 1536724, -3268842, 2079312, -7013266, 23140282, -28227510, 24133668, -56293910, 288065712, -704485126, 629862288, -1176210654

Offset: 0

Seiichi Manyama, Apr 24 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Cf. A303345, A303387, A303396, A303438.

nmax = 30; CoefficientList[Series[Exp[Sum[(1 - (-1)^j) / (j*(1 - 1/(2^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-2^k*x^k)/(1+2^k*x^k))^(1/2^k)))

A303442 Expansion of Product_{k>=1} ((1 + 4^kx^k)/(1 - 4^kx^k))^(1/4^k).

Original entry on oeis.org

1, 2, 4, 18, 34, 166, 544, 2222, 5396, 29622, 101276, 411206, 1170986, 5435466, 20007472, 90854146, 253956882, 1160301990, 4412414972, 18080729238, 56012061494, 275783908498, 1010620487696, 4103148863306, 12730394683264, 58227896627114, 223877604671508

Offset: 0

Seiichi Manyama, Apr 24 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A303361, A303438, A303443.

nmax = 30; CoefficientList[Series[Exp[Sum[((-1)^j - 1) / (j*(1 - 1/(4^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+4^k*x^k)/(1-4^k*x^k))^(1/4^k)))

A303443 Expansion of Product_{k>=1} ((1 + 8^kx^k)/(1 - 8^kx^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

Seiichi Manyama, Apr 24 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A303381, A303438, A303442.

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 *)

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)))

cp's OEIS Frontend

A303439 Expansion of Product_{k>=1} ((1 - 2^kx^k)/(1 + 2^kx^k))^(1/2^k).

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A303442 Expansion of Product_{k>=1} ((1 + 4^kx^k)/(1 - 4^kx^k))^(1/4^k).

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A303443 Expansion of Product_{k>=1} ((1 + 8^kx^k)/(1 - 8^kx^k))^(1/8^k).

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cp's OEIS Frontend

A303439 Expansion of Product_{k>=1} ((1 - 2^k*x^k)/(1 + 2^k*x^k))^(1/2^k).

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PARI

A303442 Expansion of Product_{k>=1} ((1 + 4^k*x^k)/(1 - 4^k*x^k))^(1/4^k).

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PARI

A303443 Expansion of Product_{k>=1} ((1 + 8^k*x^k)/(1 - 8^k*x^k))^(1/8^k).

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PARI

A303439 Expansion of Product_{k>=1} ((1 - 2^kx^k)/(1 + 2^kx^k))^(1/2^k).

A303442 Expansion of Product_{k>=1} ((1 + 4^kx^k)/(1 - 4^kx^k))^(1/4^k).

A303443 Expansion of Product_{k>=1} ((1 + 8^kx^k)/(1 - 8^kx^k))^(1/8^k).