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 31-38 of 38 results.

A159889 Numerator of Hermite(n, 16/23).

Original entry on oeis.org

1, 32, -34, -68800, -2093684, 224163712, 18248827144, -839028775168, -161999734633840, 1917548044739072, 1603923010615074784, 31037878026343011328, -17673243900695263973696, -959600704244699318978560, 212370574074332282486900864, 21009464001651119352291258368
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 32/23, -34/529, -68800/12167, -2093684/279841..

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(32/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018
  • Mathematica
    Numerator[Table[HermiteH[n,16/23],{n,0,40}]] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Table[23^n*HermiteH[n, 16/23], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 16/23)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 23^n * Hermite(n, 16/23).
E.g.f.: exp(32*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159904 Numerator of Hermite(n, 17/23).

Original entry on oeis.org

1, 34, 98, -68612, -2643860, 200474744, 20802160696, -565340211248, -173282369297008, -1106561008095200, 1612371646170873376, 66528051435456910784, -16502827469331089383232, -1405736274981817978343552, 179184855663797992113292160, 26914050797599819627076625664
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 34/23, 98/529, -68612/12167, -2643860/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(34/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    HermiteH[Range[0,20],17/23]//Numerator (* Harvey P. Dale, Apr 08 2018 *)
Table[23^n*HermiteH[n, 17/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(34*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 17/23).
E.g.f.: exp(34*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159921 Numerator of Hermite(n, 18/23).

Original entry on oeis.org

1, 36, 238, -67608, -3189300, 171302256, 23038278216, -258048705312, -179911241858928, -4292680465160640, 1558578348234929376, 101525379857857028736, -14483821141875255043392, -1810383783782862018394368, 134036659769169225204616320, 31640724357081844323823566336
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 36/23, 238/529, -67608/12167, -3189300/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(36/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 18/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 18/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 18/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(36*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 18/23).
E.g.f.: exp(36*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159943 Numerator of Hermite(n, 19/23).

Original entry on oeis.org

1, 38, 386, -65740, -3723284, 136726888, 24891794104, 77945890928, -181386683278960, -7552427985415072, 1440171734736484384, 134631214005677868352, -11644732516647446263616, -2151777728648689174614400, 78394097345318787274427264, 34851107415866497970816728832
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 38/23, 386/529, -65740/12167, -3723284/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(38/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],19/23]] (* Harvey P. Dale, Jan 18 2012 *)
Table[23^n*HermiteH[n,19/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 19/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(38*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 19/23).
E.g.f.: exp(38*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159946 Numerator of Hermite(n, 20/23).

Original entry on oeis.org

1, 40, 542, -62960, -4238708, 96898400, 26298701320, 436837009600, -177294701591920, -10789176512931200, 1256633088041014240, 164414811028452665600, -8048103437483217101120, -2409334578316563726502400, 14320231546481618948708480, 36259873035884206674901888000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 40/23, 542/529, -62960/12167, -4238708/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(40/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 20/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 20/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 20/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(40*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 20/23).
E.g.f.: exp(40*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159947 Numerator of Hermite(n, 21/23).

Original entry on oeis.org

1, 42, 706, -59220, -4728084, 52039512, 27197223864, 811936580112, -167321303572080, -13899725964095328, 1009444962121341984, 189455789109224933568, -3790777326580730799936, -2564543346247110450176640, -55572469192587267485099136, 35651972338523534753642227968
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 42/23, 706/529, -59220/12167, -4728084/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(42/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],21/23]] (* Harvey P. Dale, Dec 18 2015 *)
Table[23^n * HermiteH[n, 21/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 21/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(42*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 21/23).
E.g.f.: exp(42*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159948 Numerator of Hermite(n, 22/23).

Original entry on oeis.org

1, 44, 878, -54472, -5183540, 2449744, 27528715336, 1195712499872, -151266315784048, -16776228493414720, 702203805185457376, 208389464888487862144, 996888570345112992448, -2601849549129056926112512, -128192585558205188847080320, 32898121757138562880306993664
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 44/23, 878/529, -54472/12167, -5183540/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(44/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 22/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 22/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 22/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(44*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 22/23).
E.g.f.: exp(44*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A165844 Totally multiplicative sequence with a(p) = 23.

Original entry on oeis.org

1, 23, 23, 529, 23, 529, 23, 12167, 529, 529, 23, 12167, 23, 529, 529, 279841, 23, 12167, 23, 12167, 529, 529, 23, 279841, 529, 529, 12167, 12167, 23, 12167, 23, 6436343, 529, 529, 529, 279841, 23, 529, 529, 279841, 23, 12167, 23, 12167, 12167
Offset: 1

Views

Author

Jaroslav Krizek, Sep 28 2009

Keywords

Links

Programs

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

Formula

a(n) = A009967(A001222(n)) = 23^bigomega(n) = 23^A001222(n).
Previous Showing 31-38 of 38 results.

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

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