A265834 -id:A265834 - cp's OEIS frontend

A265831 Expansion of Product_{k>=1} 1/(1 - (5k-1)x^(5*k-1)).

1, 0, 0, 0, 4, 0, 0, 0, 16, 9, 0, 0, 64, 36, 14, 0, 256, 144, 137, 19, 1024, 576, 548, 202, 4120, 2304, 2192, 1537, 16847, 9245, 8768, 6148, 68522, 37462, 35106, 24592, 280649, 153151, 141382, 98407, 1122596, 622810, 572610, 394796, 4490428, 2550289, 2320167

Offset: 0

Vaclav Kotesovec, Dec 16 2015

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Cf. A067553, A265820, A265821, A265828, A265829, A265830.

Cf. A265832, A265833, A265834.

nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-1)*x^(5*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]

a(n) ~ c * 4^(n/4), where
c = 1.073840819469157289995715447280332198042213811468819293923... if mod(n,4) = 0
c = 0.431347264451907652131063891031332936177772975542057097666... if mod(n,4) = 1
c = 0.283892524489889292147114138438462508437169743150135175791... if mod(n,4) = 2
c = 0.139829615705558896416806329024657454417365487147024035166... if mod(n,4) = 3.

A265832 Expansion of Product_{k>=1} 1/(1 - (5k-2)x^(5*k-2)).

Original entry on oeis.org

1, 0, 0, 3, 0, 0, 9, 0, 8, 27, 0, 24, 81, 13, 72, 243, 103, 216, 747, 309, 648, 2345, 927, 1967, 7547, 2781, 6214, 22641, 8371, 19474, 67923, 25531, 62518, 203802, 79097, 187554, 612253, 243947, 562700, 1842300, 764609, 1689142, 5546932, 2293870, 5077244

Offset: 0

Vaclav Kotesovec, Dec 16 2015

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Cf. A067553, A265820, A265821, A265828, A265829, A265830.

Cf. A265831, A265833, A265834.

nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-2)*x^(5*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

a(n) ~ c * 3^(n/3), where
c = 1.171555591294550584937080627149625982761747171861533383233... if mod(n,3) = 0
c = 0.337047816440008855542662141834272219461954848118918717600... if mod(n,3) = 1
c = 0.518706292284531581251050944157928147536875425948432140453... if mod(n,3) = 2.

A265833 Expansion of Product_{k>=1} 1/(1 - (5k-3)x^(5*k-3)).

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 8, 7, 16, 14, 32, 28, 76, 56, 201, 112, 402, 241, 804, 566, 1608, 1475, 3238, 2950, 6739, 5900, 14066, 11827, 30533, 24012, 61066, 49865, 122164, 103846, 245070, 224499, 494374, 449035, 1001635, 898992, 2032082, 1805626, 4181855, 3640890

Offset: 0

Vaclav Kotesovec, Dec 16 2015

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Cf. A067553, A265820, A265821, A265828, A265829, A265830.

Cf. A265831, A265832, A265834.

nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-3)*x^(5*k-3)), {k, 1, nmax}], {x, 0, nmax}], x]

a(n) ~ c * 2^(n/2), where
c = 2.083307142076305100818196347525098347528893162823662452462... if n is even,
c = 1.350596787589129261746699661559125050005090208149022621867... if n is odd.

cp's OEIS Frontend

A265831 Expansion of Product_{k>=1} 1/(1 - (5k-1)x^(5*k-1)).

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A265832 Expansion of Product_{k>=1} 1/(1 - (5k-2)x^(5*k-2)).

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A265833 Expansion of Product_{k>=1} 1/(1 - (5k-3)x^(5*k-3)).

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cp's OEIS Frontend

A265831 Expansion of Product_{k>=1} 1/(1 - (5*k-1)*x^(5*k-1)).

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Formula

A265832 Expansion of Product_{k>=1} 1/(1 - (5*k-2)*x^(5*k-2)).

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Author

Keywords

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Programs

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A265833 Expansion of Product_{k>=1} 1/(1 - (5*k-3)*x^(5*k-3)).

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A265831 Expansion of Product_{k>=1} 1/(1 - (5k-1)x^(5*k-1)).

A265832 Expansion of Product_{k>=1} 1/(1 - (5k-2)x^(5*k-2)).

A265833 Expansion of Product_{k>=1} 1/(1 - (5k-3)x^(5*k-3)).