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 11-13 of 13 results.

A154307 a(n) = (n+1)^4*(4+n)!/24.

Original entry on oeis.org

1, 80, 2430, 53760, 1050000, 19595520, 363031200, 6812467200, 130947062400, 2594592000000, 53182390060800, 1129830653952000, 24898991749632000, 569337009905664000, 13505007035520000000, 332172220849717248000
Offset: 0

Views

Author

Omar E. Pol, Jan 06 2009

Keywords

Comments

Row 4 of square array A152818.

Crossrefs

Programs

  • Magma
    [(n+1)^4*Factorial(4+n)/24: n in [0..20]]; // Vincenzo Librandi, Sep 11 2016
  • Mathematica
    Table[(n + 1)^4*(4 + n)!/24, {n, 0, 25}] (* G. C. Greubel, Sep 10 2016 *)

Formula

E.g.f.: (1 + 71*x + 531*x^2 + 821*x^3 + 256*x^4)/(1-x)^9. - R. J. Mathar, Dec 21 2011

Extensions

Extended by Max Alekseyev, Apr 13 2009

A154308 a(n) = (n+1)^5*(5+n)!/120.

Original entry on oeis.org

1, 192, 10206, 344064, 9450000, 235146240, 5590680480, 130799370240, 3064161260160, 72648576000000, 1755018872006400, 43385497111756800, 1100535435333734400, 28694585299245465600, 769785401024640000000, 21259022134381903872000, 604515265659140419584000, 17698965059877321572352000
Offset: 0

Views

Author

Omar E. Pol, Jan 06 2009

Keywords

Comments

Row 5 of square array A152818.

Crossrefs

Programs

  • Magma
    [(n+1)^5*Factorial(5+n)/120: n in [0..20]]; // Vincenzo Librandi, Sep 11 2016
    
  • Mathematica
    Table[(n + 1)^5*(5 + n)!/120, {n, 0, 25}] (* G. C. Greubel, Sep 10 2016 *)
  • PARI
    for(n=0,25, print1((n+1)^5*(5+n)!/120, ", ")) \\ G. C. Greubel, Nov 24 2017

Formula

a(n) = A000142(n+1)*A000583(n+1)*A000389(n+5). - R. J. Mathar, Jan 17 2009
E.g.f.: (1 + 181*x + 3046*x^2 + 11606*x^3 + 12281*x^4 + 3125*x^5)/(1-x)^11. - R. J. Mathar, Dec 21 2011

Extensions

More terms from R. J. Mathar, Jan 17 2009

A154128 a(n) = 5^n*(n+4)!/n!.

Original entry on oeis.org

24, 600, 9000, 105000, 1050000, 9450000, 78750000, 618750000, 4640625000, 33515625000, 234609375000, 1599609375000, 10664062500000, 69726562500000, 448242187500000, 2838867187500000, 17742919921875000, 109588623046875000
Offset: 0

Views

Author

Omar E. Pol, Jan 05 2009

Keywords

Comments

Column 4 of square array A152818.

Crossrefs

Programs

  • Magma
    [5^n*(n+4)*(n+3)*(n+2)*(n+1): n in [0..20]]; // Vincenzo Librandi, Aug 15 2011
  • Mathematica
    LinearRecurrence[{25, -250, 1250, -3125, 3125}, {24, 600, 9000, 105000, 1050000}, 25] (* or *) Table[5^n*(n+4)*(n+3)*(n+2)*(n+1), {n,0,25}] (* G. C. Greubel, Sep 02 2016 *)

Formula

a(n) = 5^n*(n+4)*(n+3)*(n+2)*(n+1).
From R. J. Mathar, Feb 06 2009: (Start)
a(n) = A052762(n+4)*A000351(n).
a(n) = 24*A036071(n).
G.f: 24/(1-5*x)^5. (End)
From G. C. Greubel, Sep 02 2016: (Start)
a(n) = 25*a(n-1) - 250*a(n-2) + 1250*a(n-3) - 3125*a(n-4) + 3125*a(n-5).
E.g.f.: (24 + 480*x + 1800*x^2 + 2000*x^3 + 625*x^4)*exp(5*x). (End)

Extensions

More terms from R. J. Mathar, Feb 06 2009
Previous Showing 11-13 of 13 results.