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 1-5 of 5 results.

A159197 Numerator of Hermite(n, 2/9).

Original entry on oeis.org

1, 4, -146, -1880, 63436, 1471984, -45495224, -1612749344, 45140586640, 2270685496384, -56732233335584, -3905439437484416, 85475082054073024, 7934074594685996800, -148274224427133801344, -18587578078456375947776, 285956053044109633474816
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159030.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018
  • Mathematica
    Numerator[Table[HermiteH[n,2/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
  • PARI
    a(n)=numerator(polhermite(n,2/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 10 2018: (Start)
a(n) = 9^n * Hermite(n,2/9).
E.g.f.: exp(4*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159232 Numerator of Hermite(n, 4/9).

Original entry on oeis.org

1, 8, -98, -3376, 20620, 2352608, 2118664, -2269785664, -20560850288, 2777155418240, 52194963065824, -4081432073022208, -125662880767476032, 6929000903815364096, 320078034126827436160, -13154349776838626280448, -883024421142899680112384
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159030, A159197.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(8/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018
  • Mathematica
    Numerator[Table[HermiteH[n,4/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)
  • PARI
    a(n)=numerator(polhermite(n,4/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)
a(n) = 9^n * Hermite(n, 4/9).
E.g.f.: exp(8*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159240 Numerator of Hermite(n, 5/9).

Original entry on oeis.org

1, 10, -62, -3860, -8468, 2416600, 31025080, -2038684400, -55569284720, 2086442135200, 101884438473760, -2361191874286400, -205169988103104320, 2538457122581718400, 457472566170954881920, -1182495092305788512000, -1123483286718478248185600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159030, A159197.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018
  • Mathematica
    Numerator[Table[HermiteH[n,5/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)
  • PARI
    a(n)=numerator(polhermite(n,5/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)
a(n) = 9^n * Hermite(n, 5/9).
E.g.f.: exp(10*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159242 Numerator of Hermite(n, 7/9).

Original entry on oeis.org

1, 14, 34, -4060, -73364, 1603784, 81877816, -412588624, -98625684080, -846044720416, 131951621302816, 3217915145313344, -190086977127231296, -8916844722270378880, 275487347718163805056, 24080226698163512570624, -332311081180848870297344
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159030, A159197.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018
  • Mathematica
    Numerator[Table[HermiteH[n,7/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)
  • PARI
    a(n)=numerator(polhermite(n,7/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)
a(n) = 9^n * Hermite(n, 7/9).
E.g.f.: exp(14*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159245 Numerator of Hermite(n, 8/9).

Original entry on oeis.org

1, 16, 94, -3680, -104564, 711616, 96082696, 845632384, -95427659120, -2622782115584, 97169013147616, 5803611237607936, -80297401627324736, -12566978671947023360, -31965330924006479744, 27990462333191745304576, 525523151476403670651136
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Comments

Denominators are A001019. - Robert Israel, Jun 07 2018

Links

Crossrefs

Cf. A001019, A159030, A159197.

Programs

Formula

From Robert Israel, Jun 07 2018: (Start)
E.g.f.: exp(16*x-81*x^2).
a(n+2)=16*a(n+1)-162*(n+1)*a(n). (End)
Showing 1-5 of 5 results.

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

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