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 11-20 of 31 results. Next

A160107 Numerator of Hermite(n, 7/27).

Original entry on oeis.org

1, 14, -1262, -58492, 4701100, 406940744, -28573848584, -3959951508688, 236185377526672, 49495469682710240, -2406287948347046624, -755331979250773951936, 28017398406079098428608, 13607531886656648441072768, -340536322975630153440817280
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 14/27, -1262/729, -58492/19683, 4701100/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    HermiteH[Range[0,20],7/27]//Numerator (* Harvey P. Dale, Jun 08 2018 *)
Table[27^n*HermiteH[n, 7/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 7/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(14*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 7/27).
E.g.f.: exp(14*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160131 Numerator of Hermite(n, 8/27).

Original entry on oeis.org

1, 16, -1202, -65888, 4203340, 451512256, -23418152504, -4324519655552, 169813349966992, 53158210861830400, -1377759404477582624, -797090864837128553984, 9343051491617413259968, 14095390595056279792663552, 48438051548784025753183360, -286940104001508238715797489664
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 16/27, -1202/729, -65888/19683, 4203340/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(16/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 8/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 8/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(16*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 8/27).
E.g.f.: exp(16*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160132 Numerator of Hermite(n, 10/27).

Original entry on oeis.org

1, 20, -1058, -79480, 3038092, 524289200, -11661906680, -4819720055200, 22627018472080, 56669755093294400, 836483365475254240, -809515361950727267200, -29605827454506672845120, 13571164223599790810028800, 832572138044715293306980480
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 20/27, -1058/729, -79480/19683, 3038092/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Numerator/@(HermiteH[#,10/27]&/@Range[0,20])  (* Harvey P. Dale, Mar 30 2011 *)
Table[27^n*HermiteH[n, 10/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 10/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(20*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 10/27).
E.g.f.: exp(20*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160139 Numerator of Hermite(n, 11/27).

Original entry on oeis.org

1, 22, -974, -85580, 2377516, 551407912, -5201117576, -4938141000848, -55556496038000, 56376233721055072, 1969289482873847584, -778641119029758302912, -48713569344985450216256, 12551406492954971362990720, 1199447936209863593384712064
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 22/27, -974/729, -85580/19683, 2377516/531441, ...

Links

Crossrefs

Cf. A009971 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],11/27]] (* Harvey P. Dale, Mar 06 2014 *)
Table[27^n*HermiteH[n, 11/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(22*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 11/27).
E.g.f.: exp(22*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160140 Numerator of Hermite(n, 13/27).

Original entry on oeis.org

1, 26, -782, -96148, 920620, 584671256, 8490132856, -4893960693232, -213893273952368, 51521932403096480, 4146277783283481376, -643386552071776162624, -83226053442166654536512, 9092813725551462723320192, 1813879773807164800891373440
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 26/27, -782/729, -96148/19683, 920620/531441

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 13/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 13/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(26*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 13/27).
E.g.f.: exp(26*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160141 Numerator of Hermite(n, 14/27).

Original entry on oeis.org

1, 28, -674, -100520, 133516, 589971088, 15545858824, -4725783030752, -290982960018800, 46974010390164928, 5133550692291311584, -541141652104447925888, -97483852261892597109056, 6738266481886428192282880, 2036380397264732274988968064, -80522844304853268561187040768
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 28/27, -674/729, -100520/19683, 133516/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 14/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 14/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(28*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 14/27).
E.g.f.: exp(28*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160142 Numerator of Hermite(n, 16/27).

Original entry on oeis.org

1, 32, -434, -107200, -1532084, 576163712, 29606131144, -4092883955968, -433132461046640, 33879159708918272, 6767697264539394784, -277391836090767772672, -117416867483587382271296, 1095907804769276717987840, 2260588356036532098545755264
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 32/27, -434/729, -107200/19683, -1532084/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(32/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 16/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 16/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(32*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 16/27).
E.g.f.: exp(32*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160146 Numerator of Hermite(n, 17/27).

Original entry on oeis.org

1, 34, -302, -109412, -2399060, 556522744, 36410920696, -3630489660848, -495046505092208, 25514450230996000, 7363491547673817376, -121641971747011889216, -122231504480991087309632, -2027623214667976954804352, 2247836746633993852403416960
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 34/27, -302/729, -109412/19683, -2399060/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(34/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 17/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(34*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 17/27).
E.g.f.: exp(34*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160147 Numerator of Hermite(n, 19/27).

Original entry on oeis.org

1, 38, -14, -111340, -4169684, 490886888, 49050698104, -2430351968272, -592964799643760, 5814962971461728, 8001852693840964384, 219288242242044652352, -120000760298623690001216, -8396695977614513457596800, 1955419963550761908894369664
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 38/27, -14/729, -111340/19683, -4169684/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(38/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 19/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 19/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(38*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 19/27).
E.g.f.: exp(38*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160148 Numerator of Hermite(n, 20/27).

Original entry on oeis.org

1, 40, 142, -110960, -5059508, 444738400, 54673349320, -1703637550400, -626141705175920, -5174439819171200, 8009253862551574240, 395813487065579065600, -112619873964978985037120, -11429947728298530733222400, 1677399182000270453064676480
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 40/27, 142/729, -110960/19683, -5059508/531441, ...

Links

Crossrefs

Cf. A009971 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(40/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
  • Mathematica
    Table[27^n*HermiteH[n, 20/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 20/27)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(40*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 20/27).
E.g.f.: exp(40*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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