A303440 -id:A303440 - cp's OEIS frontend

A303441 Expansion of Product_{k>=1} ((1 - (2^kx)^k)/(1 + (2^kx)^k))^(1/2^k).

1, -2, -6, -116, -7914, -2080044, -2143234268, -8791784539464, -144097582730402202, -9444444682320960008908, -2475861188239098437867827380, -2596143477450571483513272599120280, -10889030549158315918778789768740624543108

Offset: 0

Seiichi Manyama, Apr 24 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..58

Cf. A303306, A303394, A303395, A303440.

N=20; x='x+O('x^N); Vec(prod(k=1, N, ((1-(2^k*x)^k)/(1+(2^k*x)^k))^(1/2^k)))

a(n) ~ -2^(n^2 - n + 1). - Vaclav Kotesovec, Apr 25 2018

A303444 Expansion of Product_{k>=1} ((1 + (4^kx)^k)/(1 - (4^kx)^k))^(1/4^k).

Original entry on oeis.org

1, 2, 34, 8268, 33571414, 2199090644476, 2305847408435939284, 38685630839429196310146392, 10384593794440986129804618334166246, 44601490417830435032541177335778584157585132, 3064991081820980697863893053179715579559319341564967996, 3369993333399959956498356892070248429341537193850764394491913892776

Offset: 0

Seiichi Manyama, Apr 24 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..41

Cf. A303440, A303445.

N=20; x='x+O('x^N); Vec(prod(k=1, N, ((1+(4^k*x)^k)/(1-(4^k*x)^k))^(1/4^k)))

a(n) ~ 2^(2*n^2 - 2*n + 1). - Vaclav Kotesovec, Apr 25 2018

A303445 Expansion of Product_{k>=1} ((1 + (8^kx)^k)/(1 - (8^kx)^k))^(1/8^k).

Original entry on oeis.org

1, 2, 130, 524588, 137440010582, 2305843284159782076, 2475880083182464573602036628, 170141183465420992188660515119769982616, 748288838313762576487529438443476930331940262147046

Offset: 0

Seiichi Manyama, Apr 24 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..33

Cf. A303440, A303444.

N=20; x='x+O('x^N); Vec(prod(k=1, N, ((1+(8^k*x)^k)/(1-(8^k*x)^k))^(1/8^k)))

a(n) ~ 2^(3*n^2 - 3*n + 1). - Vaclav Kotesovec, Apr 25 2018

cp's OEIS Frontend

A303441 Expansion of Product_{k>=1} ((1 - (2^kx)^k)/(1 + (2^kx)^k))^(1/2^k).

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A303444 Expansion of Product_{k>=1} ((1 + (4^kx)^k)/(1 - (4^kx)^k))^(1/4^k).

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A303445 Expansion of Product_{k>=1} ((1 + (8^kx)^k)/(1 - (8^kx)^k))^(1/8^k).

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cp's OEIS Frontend

A303441 Expansion of Product_{k>=1} ((1 - (2^k*x)^k)/(1 + (2^k*x)^k))^(1/2^k).

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A303444 Expansion of Product_{k>=1} ((1 + (4^k*x)^k)/(1 - (4^k*x)^k))^(1/4^k).

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Author

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PARI

Formula

A303445 Expansion of Product_{k>=1} ((1 + (8^k*x)^k)/(1 - (8^k*x)^k))^(1/8^k).

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A303441 Expansion of Product_{k>=1} ((1 - (2^kx)^k)/(1 + (2^kx)^k))^(1/2^k).

A303444 Expansion of Product_{k>=1} ((1 + (4^kx)^k)/(1 - (4^kx)^k))^(1/4^k).

A303445 Expansion of Product_{k>=1} ((1 + (8^kx)^k)/(1 - (8^kx)^k))^(1/8^k).