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 11-15 of 15 results.

A127369 (n^3+n)*4^n.

Original entry on oeis.org

8, 160, 1920, 17408, 133120, 909312, 5734400, 34078720, 193462272, 1059061760, 5628755968, 29192355840, 148310589440, 740344987648, 3639984783360, 17660905521152, 84696755077120, 402008938905600, 1890610243960832
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Crossrefs

Programs

  • Magma
    [(n^3 + n) * 4^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) 4^n, {n, 20}] (* Vincenzo Librandi Feb 22 2013 *)
    LinearRecurrence[{16,-96,256,-256},{8,160,1920,17408},20] (* Harvey P. Dale, Aug 14 2021 *)

Formula

G.f.: 8*x*(1+4*x+16*x^2)/(1-4*x)^4. [R. J. Mathar, Dec 19 2008]

A128013 a(n) = (n^3 +n)*5^n.

Original entry on oeis.org

10, 250, 3750, 42500, 406250, 3468750, 27343750, 203125000, 1441406250, 9863281250, 65527343750, 424804687500, 2697753906250, 16833496093750, 103454589843750, 627441406250000, 3761291503906250, 22315979003906250
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Crossrefs

Programs

  • Magma
    [(n^3 + n)*5^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
    
  • Magma
    I:=[10,250,3750,42500]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013
    
  • Mathematica
    Table[(n^3 + n) 5^n, {n, 30}] (* or *) CoefficientList[Series[10 (1 + 5 x + 25 x^2)/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)
  • PARI
    for(n=1, 30, print1((n^3 +n)*5^n, ", ")) \\ G. C. Greubel, May 08 2018

Formula

G.f.: 10*x(1+5*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi, Feb 22 2013
a(n) = 20*a(n-1) -150*a(n-2) +500*a(n-3) -625*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128043 (n^3+n)*6^n.

Original entry on oeis.org

12, 360, 6480, 88128, 1010880, 10357632, 97977600, 873400320, 7437339648, 61070837760, 486873649152, 3787601264640, 28864133775360, 216128364576768, 1593927097712640, 11600403939459072, 83448431062548480
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Crossrefs

Programs

  • Magma
    [(n^3 + n)*6^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) * 6^n, {n, 30}] (* or *) CoefficientList[Series[12 (1 + 6 x + 36 x^2)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 12*x*(1 + 6*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 22 2013

A128048 (n^3+n)*8^n.

Original entry on oeis.org

16, 640, 15360, 278528, 4259840, 58195968, 734003200, 8724152320, 99052683264, 1084479242240, 11527692222464, 119571889520640, 1214960348692480, 12129812277624832, 119275021381140480, 1157425104234217472
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Crossrefs

Programs

  • Magma
    [(n^3 + n)*8^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
    
  • Magma
    I:=[16,640,15360,278528]; [n le 4 select I[n] else 32*Self(n-1)-384*Self(n-2)+2048*Self(n-3)-4096*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013
  • Mathematica
    Table[(n^3 + n) 8^n, {n, 30}] (* or *) CoefficientList[Series[16 (1 + 8 x + 64 x^2)/(1 - 8 x)^4, {x, 0, 20}],x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 16*x*(1+8*x+64*x^2)/(1-8*x)^4. - Vincenzo Librandi, Feb 22 2013
a(n) = 32*a(n-1) -384*a(n-2) +2048*a(n-3) -4096*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128051 (n^3+n)*7^n.

Original entry on oeis.org

14, 490, 10290, 163268, 2184910, 26118078, 288240050, 2997696520, 29780961966, 285300001490, 2653572489106, 24083839729740, 214124712999470, 1870539234917542, 16094233518706770, 136653810502199312
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Crossrefs

Programs

  • Magma
    [(n^3 + n)*7^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) * 7^n, {n, 30}] (* or *) CoefficientList[Series[14 (1 + 7 x + 49 x^2)/(1 - 7 x)^4, {x, 0, 20}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 14*x*(1 + 7*x + 49*x^2)/(1 - 7*x)^4. - Vincenzo Librandi, Feb 22 2013
Previous Showing 11-15 of 15 results.