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.

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A160194 Numerator of Hermite(n, 9/28).

Original entry on oeis.org

1, 9, -311, -9855, 277041, 17946009, -381486279, -45642389679, 636016842465, 148858685615529, -904139249676759, -591663300859964511, -1426321263133495791, 2770347275877071597625, 32201658639821938929561, -14913850922254971477399951, -323570411102447744202418239
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 9/14, -311/196, -9855/2744, 277041/38416, ...

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(9/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 9/28], {n, 0, 30}]] (* or *) Table[14^n* HermiteH[n, 9/28], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 9/28)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)
a(n) = 14^n * Hermite(n, 9/28).
E.g.f.: exp(9*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160195 Numerator of Hermite(n, 11/28).

Original entry on oeis.org

1, 11, -271, -11605, 191041, 20298091, -151161359, -49403884981, -128655965695, 153515367677771, 2142567291427441, -578212001091160469, -15599082172637890751, 2548319349233802047915, 107524435593334513794161, -12802407797068425987221749
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 11/14, -271/196, -11605/2744, 191041/38416, ...

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(11/14)^(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[14^n*HermiteH[n, 11/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(11*x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 14^n * Hermite(n, 11/28).
E.g.f.: exp(11*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160196 Numerator of Hermite(n, 13/28).

Original entry on oeis.org

1, 13, -223, -13091, 92065, 21723533, 101958529, -49768288739, -926761957183, 144025448042125, 5141947009489249, -497734445201769763, -28642623292540648607, 1968988727426096533261, 171559661755326400233665, -8575534533295174571498723, -1120252760054156502803433599
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 13/14, -223/196, -13091/2744, 92065/38416, ...

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(13/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 25 2018
  • Mathematica
    Table[14^n*HermiteH[n, 13/28], {n, 0, 30}] (* G. C. Greubel, Sep 25 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 13/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(13*x - 196*x^2))) \\ G. C. Greubel, Sep 25 2018

Formula

From G. C. Greubel, Sep 25 2018: (Start)
a(n) = 14^n * Hermite(n, 13/28).
E.g.f.: exp(13*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160197 Numerator of Hermite(n, 15/28).

Original entry on oeis.org

1, 15, -167, -14265, -17583, 22103775, 366019305, -46497789225, -1701823811295, 120289709840175, 7808380053851385, -354409961765715225, -38985884218692900495, 1082356196865530910975, 214907408931441984587145, -2716359674426403870623625
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 15/14, -167/196, -14265/2744, -17583/38416, ...

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(15/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 25 2018
  • Mathematica
    Table[14^n*HermiteH[n, 15/28], {n, 0, 30}] (* G. C. Greubel, Sep 25 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 15/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(15*x - 196*x^2))) \\ G. C. Greubel, Sep 25 2018

Formula

From G. C. Greubel, Sep 25 2018: (Start)
a(n) = 14^n * Hermite(n, 15/28).
E.g.f.: exp(15*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160219 Numerator of Hermite(n, 17/28).

Original entry on oeis.org

1, 17, -103, -15079, -135215, 21345217, 627890089, -39529818871, -2394937325023, 83251577454065, 9864615699400249, -158647716730130567, -45233234080226093327, -22686119865309399391, 230122896835121911804745, 4036590672017890484538473
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 17/14, -103/196, -15079/2744, -135215/38416

Links

Crossrefs

Cf. A001023 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(17/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 17/28], {n, 0, 50}]] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(17*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 14^n * Hermite(n, 17/28).
E.g.f.: exp(17*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160220 Numerator of Hermite(n, 19/28).

Original entry on oeis.org

1, 19, -31, -15485, -257759, 19383059, 873485761, -28992725309, -2947706709055, 34914759096979, 11062889692388641, 73329048495226499, -46309928432170516511, -1224828484332785265005, 212723654088018032104961, 10763608149690668144341699, -1046306531193423334034678399
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 19/14, -31/196, -15485/2744, -257759/38416

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(19/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],19/28]] (* Harvey P. Dale, Jul 26 2015 *)
Table[14^n*HermiteH[n, 19/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 19/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(19*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 14^n * Hermite(n, 19/28).
E.g.f.: exp(19*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160221 Numerator of Hermite(n, 23/28).

Original entry on oeis.org

1, 23, 137, -14881, -503375, 11755783, 1256998009, 1261352591, -3420191427103, -82620004548745, 10166175250198249, 557692448585640127, -31009621361385126767, -3336606569458709073049, 81283079360068297324505, 20180807678470966231356527, -13785930032369364946889279
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 23/14, 137/196, -14881/2744, -503375/38416

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(23/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[14^n*HermiteH[n, 23/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 23/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(23*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 14^n * Hermite(n, 23/28).
E.g.f.: exp(23*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160222 Numerator of Hermite(n, 25/28).

Original entry on oeis.org

1, 25, 233, -13775, -618383, 6139625, 1365521305, 19697634625, -3254549595295, -143135522066375, 7903662920541385, 758682819513724625, -15113524025531336495, -3946682083630844048375, -21648533656663410430855, 21118177933549486876710625
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 25/14, 233/196, -13775/2744, -618383/38416

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(25/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[14^n*HermiteH[n, 25/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 25/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(25*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 14^n * Hermite(n, 25/28).
E.g.f.: exp(25*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(25/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160223 Numerator of Hermite(n, 27/28).

Original entry on oeis.org

1, 27, 337, -12069, -722175, -574533, 1399950609, 39149968059, -2784415333503, -197953513837605, 4478672422983249, 896901929663959323, 4904316613023132033, -4086610128587640090501, -135330870931832163283695, 18773382870529500408009723
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 27/14, 337/196, -12069/2744, -722175/38416

Links

Crossrefs

Cf. A001023 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(27/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[14^n*HermiteH[n, 27/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 27/28)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(27*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 14^n * Hermite(n, 27/28).
E.g.f.: exp(27*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(27/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

A165835 Totally multiplicative sequence with a(p) = 14.

Original entry on oeis.org

1, 14, 14, 196, 14, 196, 14, 2744, 196, 196, 14, 2744, 14, 196, 196, 38416, 14, 2744, 14, 2744, 196, 196, 14, 38416, 196, 196, 2744, 2744, 14, 2744, 14, 537824, 196, 196, 196, 38416, 14, 196, 196, 38416, 14, 2744, 14, 2744, 2744, 196, 14, 537824, 196, 2744
Offset: 1

Views

Author

Jaroslav Krizek, Sep 28 2009

Keywords

Links

Programs

  • Mathematica
    14^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)

Formula

a(n) = A001023(A001222(n)) = 14^bigomega(n) = 14^A001222(n).
Previous Showing 21-30 of 33 results. Next

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

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