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 11-14 of 14 results.

A022667 Expansion of Product_{m>=1} (1 - m*q^m)^7.

Original entry on oeis.org

1, -7, 7, 42, -56, -105, -126, 489, 987, -651, -833, -6062, -3101, 10381, 21040, 34720, -20692, -46732, -173642, -238014, 25193, 614802, 1161951, 982667, 981253, -3028025, -5721548, -10660692, -7448428, 4778767, 21412363, 79760653, 64512273, 37376857, -64640856, -220678215
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Column k=7 of A297323.

Programs

  • Magma
    Coefficients(&*[(1-m*x^m)^7:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 24 2018
  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^7, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 24 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^7)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-7*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(31) onward added by G. C. Greubel, Feb 24 2018

A022668 Expansion of Product_{m>=1} (1 - m*q^m)^8.

Original entry on oeis.org

1, -8, 12, 48, -106, -128, 8, 880, 1041, -2560, -2524, -6720, 5030, 30880, 26696, 9264, -136524, -152456, -172604, 37824, 938316, 1568960, 1225624, -1981904, -4585531, -10791440, -8363184, 2558560, 29452194, 67002976, 59590976, 77029104, -140261287, -367505912, -536229932
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Column k=8 of A297323.

Programs

  • Magma
    Coefficients(&*[(1-m*x^m)^8:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 24 2018
  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^8, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 24 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^8)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-8*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(30) onward added by G. C. Greubel, Feb 24 2018

A022669 Expansion of Product_{m>=1} (1 - m*q^m)^9.

Original entry on oeis.org

1, -9, 18, 51, -171, -117, 249, 1251, 531, -5599, -3006, -2295, 20664, 50508, -6354, -78597, -292887, -105273, 268957, 792414, 1974312, 825753, -2605185, -9778671, -9956433, -4944978, 19214991, 57418523, 78518664, 60044976, -124946361, -247193622, -634049649, -623771424, 218263050
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Column k=9 of A297323.

Programs

  • Magma
    Coefficients(&*[(1-m*x^m)^9:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 24 2018
  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^9, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 24 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^9)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-9*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(29) onward added by G. C. Greubel, Feb 24 2018

A022684 Expansion of Product_{m>=1} (1-m*q^m)^24.

Original entry on oeis.org

1, -24, 228, -944, 114, 13920, -40824, -35568, 314943, -32016, -1256028, -1702560, 7990622, 15859872, -44241384, -69900560, 66340899, 389812176, 368445848, -1602538800, -2603154606, 114976000, 12365751792
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -24, g(n) = n. - Seiichi Manyama, Dec 29 2017

Links

Crossrefs

Column k=24 of A297323.

Programs

  • Magma
    Coefficients(&*[(1-m*x^m)^24:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Jul 19 2018
  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^24, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^24)) \\ G. C. Greubel, Jul 19 2018
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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