cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A265829 Expansion of Product_{k>=1} 1/(1 - (4*k-2)*x^(4*k-2)).

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 14, 0, 28, 0, 66, 0, 168, 0, 350, 0, 760, 0, 1754, 0, 3692, 0, 7766, 0, 17076, 0, 35282, 0, 73232, 0, 156758, 0, 320768, 0, 658978, 0, 1380612, 0, 2808534, 0, 5732780, 0, 11849002, 0, 23997576, 0, 48701918, 0, 99744056, 0, 201405042
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (4*k-2)*x^(4*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

If n is even, then a(n) ~ c * 2^(n/2), where c = 6.8748052998532604456256851165148110527112306899116599334584... .

A265830 Expansion of Product_{k>=1} 1/(1 - (4*k-3)*x^(4*k-3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 6, 6, 6, 15, 40, 40, 40, 53, 98, 223, 223, 240, 386, 611, 1236, 1257, 1459, 2189, 3314, 6464, 6891, 8630, 12280, 17934, 34094, 37282, 45977, 64260, 93317, 177015, 199516, 243028, 335386, 486558, 914525, 1027071, 1246171, 1717917, 2499859
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (4*k-3)*x^(4*k-3)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 5^(n/5), where
c = 2.507825733169876852324734244164361344346137946210165985160... if mod(n,5) = 0
c = 2.044059357237393849525094744007074653835911858380855756712... if mod(n,5) = 1
c = 1.804839638762776493150118361894215102701328815651225876275... if mod(n,5) = 2
c = 1.804038421648852594778176511112001297019074444232793470829... if mod(n,5) = 3
c = 1.892664578176041496503561133229019191251461591133509951564... if mod(n,5) = 4.

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

Original entry on oeis.org

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

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265832, A265833, A265834.

Programs

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

Formula

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 - (5*k-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

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265833, A265834.

Programs

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

Formula

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 - (5*k-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

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265832, A265834.

Programs

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

Formula

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

A265834 Expansion of Product_{k>=1} 1/(1 - (5*k-4)*x^(5*k-4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 18, 54, 54, 54, 54, 70, 136, 352, 352, 352, 373, 590, 986, 2282, 2282, 2308, 2610, 3912, 6288, 14064, 14095, 14738, 17881, 25693, 39949, 86641, 87449, 93243, 112101, 158973, 244550, 525900, 536105, 585510, 698658, 979936
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265832, A265833.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-4)*x^(5*k-4)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 6^(n/6), where
c = 1.946161573585465742120451753889110403102785483969509157884... if mod(n,6) = 0
c = 1.492695368258335848636116399838163314228018468452433528714... if mod(n,6) = 1
c = 1.205892633747241909081118546347785156858709648302505136919... if mod(n,6) = 2
c = 1.062580541177612790307764142722360963628515836057478463493... if mod(n,6) = 3
c = 1.098873691517923934789388233817534832428257891275964607033... if mod(n,6) = 4
c = 1.239744254161848837318727201496086964789190390884460407810... if mod(n,6) = 5.
Showing 1-6 of 6 results.

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