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.

A159030 Numerator of Hermite(n, 1/9).

Original entry on oeis.org

1, 2, -158, -964, 74860, 774392, -59087816, -870884656, 65263814032, 1259194142240, -92636252574176, -2225167015577152, 160627468056027328, 4646979614394038144, -328987488497205476480, -11197324742440089463552, 777044947563329128919296
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A158811, A158954, A158960, A158980.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(2/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
  • Mathematica
    Numerator[Table[HermiteH[n,1/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
  • PARI
    a(n)=numerator(polhermite(n,1/9)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    for(n=0,30, print1(9^n*polhermite(n,1/9), ", ")) \\ G. C. Greubel, Jun 10 2018

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 9^n * Hermite(n, 1/9).
E.g.f.: exp(2*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/9)^(n-2k)/(k!*(n-2k)!)). (End)

A159014 Numerator of Hermite(n, 1/8).

Original entry on oeis.org

1, 1, -31, -95, 2881, 15041, -445919, -3333791, 96552065, 950002561, -26856992159, -330857811679, 9122803428289, 136172203113025, -3658914023055199, -64664061017690399, 1691614670048805121, 34799613911106289409, -885438766595443696415
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A158811, A158954, A158960, A158980.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(1/4)^(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,1/8],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
  • PARI
    a(n)=numerator(polhermite(n,1/8)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 10 2018: (Start)
a(n) = 4^n * Hermite(n,1/8).
E.g.f.: exp(x-16*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/4)^(n-2*k)/(k!*(n-2*k)!)). (End)

A158981 Numerator of Hermite(n, 2/7).

Original entry on oeis.org

1, 4, -82, -1112, 19660, 514544, -7575224, -332852768, 3865192592, 276417340480, -2303430504224, -280102715687296, 1362687220804288, 334851542531477248, -396657349178753920, -461002945749901799936, -1260925479706838937344, 717808917017018666550272
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A158980.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018
  • Mathematica
    Numerator[Table[HermiteH[n,2/7],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[7^n*HermiteH[n, 2/7], {n,0,50}] (* G. C. Greubel, Jul 10 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,2/7)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 10 2018: (Start)
a(n) = 7^n * Hermite(n, 2/7).
E.g.f.: exp(4*x - 49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159005 Numerator of Hermite(n, 5/7).

Original entry on oeis.org

1, 10, 2, -1940, -19988, 560600, 15400120, -175631600, -12320798320, 14487191200, 11011816030240, 95920712926400, -10911530551334720, -221918063914793600, 11682109283252497280, 421292676523621792000, -12959773881144953081600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A158980.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018
  • Mathematica
    Numerator[Table[HermiteH[n,5/7],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[7^n*HermiteH[n, 5/7], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,5/7)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(10*x - 49*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 7^n * Hermite(n, 5/7).
E.g.f.: exp(10*x - 49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159013 Numerator of Hermite(n, 6/7).

Original entry on oeis.org

1, 12, 46, -1800, -35124, 284112, 20620104, 80383392, -13180790640, -221190067008, 8971176540384, 324420384152448, -5777883700704576, -450852976171733760, 1950788120636824704, 641979740755260615168, 4836098351726995067136
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A158980, A158981.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(12/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018
  • Mathematica
    Numerator[Table[HermiteH[n,6/7],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[7^n*HermiteH[n, 6/7], {n,0,30}] (* G. C. Greubel, Jul 14 2018~ *)
  • PARI
    a(n)=numerator(polhermite(n,6/7)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(12*x - 49*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 7^n * Hermite(n, 6/7).
E.g.f.: exp(12*x - 49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/7)^(n-2*k)/(k!*(n-2*k)!)). (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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