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.

Previous Showing 31-34 of 34 results.

A022592 Expansion of Product_{m>=1} (1+q^m)^28.

Original entry on oeis.org

1, 28, 406, 4088, 32249, 212772, 1222438, 6283400, 29454432, 127721972, 517920340, 1980864312, 7194850761, 24957519216, 83064794746, 266299577040, 825106028411, 2477872472348, 7230302637376, 20543975496576, 56949757063171, 154281017250160, 409072030569524
Offset: 0

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Column k=28 of A286335.

Programs

  • Magma
    Coefficients(&*[(1+x^m)^28:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 19 2018
  • Mathematica
    nmax=50; CoefficientList[Series[Product[(1+q^m)^28,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^28)) \\ G. C. Greubel, Feb 19 2018
    

Formula

a(n) ~ (7/3)^(1/4) * exp(2 * Pi * sqrt(7*n/3)) / (32768 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

A022593 Expansion of Product_{m>=1} (1+q^m)^29.

Original entry on oeis.org

1, 29, 435, 4524, 36801, 249980, 1476535, 7792619, 37464346, 166445529, 690898842, 2702690003, 10033022642, 35545708813, 120756549637, 394935306099, 1247670362782, 3818503661392, 11350088407317, 32837741707782, 92652254354675, 255382893501050, 688721602753864
Offset: 0

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Author

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Column k=29 of A286335.

Programs

  • Magma
    Coefficients(&*[(1+x^m)^29:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 19 2018
  • Mathematica
    nmax=50; CoefficientList[Series[Product[(1+q^m)^29,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^29)) \\ G. C. Greubel, Feb 19 2018
    
  • PARI
    q='q+O('q^99); Vec((eta(q^2)/eta(q))^29) \\ Altug Alkan, May 03 2018
    

Formula

a(n) ~ (29/3)^(1/4) * exp(Pi * sqrt(29*n/3)) / (65536 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

A022594 Expansion of Product_{m>=1} (1+q^m)^30.

Original entry on oeis.org

1, 30, 465, 4990, 41820, 292236, 1773325, 9603210, 47322525, 215286380, 914269641, 3656192760, 13865226845, 50148901590, 173821904265, 579696375972, 1866529110420, 5819476726230, 17613901516660, 51870170192610, 148909462006422, 417468856858550, 1144709400114480
Offset: 0

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Author

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Crossrefs

Column k=30 of A286335.

Programs

  • Magma
    Coefficients(&*[(1+x^m)^30:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 19 2018
  • Mathematica
    nmax=50; CoefficientList[Series[Product[(1+q^m)^30,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^30)) \\ G. C. Greubel, Feb 19 2018
    

Formula

a(n) ~ (5/2)^(1/4) * exp(Pi * sqrt(10*n)) / (65536 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

A022595 Expansion of Product_{m >=1} (1+q^m)^31.

Original entry on oeis.org

1, 31, 496, 5487, 47337, 340039, 2118385, 11763911, 59384158, 276491170, 1200703594, 4906332242, 18998567031, 70120824201, 247873586247, 842625902072, 2764160465375, 8776228494225, 27038961793349, 81019542614568, 236575764828149, 674366427736330, 1879524499776454
Offset: 0

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Author

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Crossrefs

Column k=31 of A286335.

Programs

  • Magma
    Coefficients(&*[(1+x^m)^31:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Mar 20 2018
  • Mathematica
    nmax=50; CoefficientList[Series[Product[(1+q^m)^31,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^31)) \\ G. C. Greubel, Mar 20 2018
    

Formula

a(n) ~ (31/3)^(1/4) * exp(Pi * sqrt(31*n/3)) / (131072 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

Extensions

Terms a(19) onward added by G. C. Greubel, Mar 20 2018
Previous Showing 31-34 of 34 results.