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 31-40 of 41 results. Next

A160282 Numerator of Hermite(n, 20/29).

Original entry on oeis.org

1, 40, -82, -137840, -5099828, 723394400, 71825329480, -4427483105600, -1022770753521520, 18665382528092800, 16229318967932481760, 335221024594778374400, -286866018560895642547520, -18240741902856832410790400, 5542982685738270823512456320
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 40/29, -82/841, -137840/24389, -5099828/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(40/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[29^n*HermiteH[n, 20/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 20/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(40*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 20/29).
E.g.f.: exp(40*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160283 Numerator of Hermite(n, 21/29).

Original entry on oeis.org

1, 42, 82, -137844, -6203220, 666879192, 80178006264, -3362668542576, -1085247924540528, -332344921799520, 16414524594978933024, 695000074573783113408, -274511530924201328046912, -25557365804013694138997376, 4929059771420011085235888000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 42/29, 82/841, -137844/24389, -6203220/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(42/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[29^n*HermiteH[n, 21/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 21/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(42*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 21/29).
E.g.f.: exp(42*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160284 Numerator of Hermite(n, 22/29).

Original entry on oeis.org

1, 44, 254, -136840, -7302644, 599343184, 87786336136, -2185972622944, -1129779117074800, -20295833536956736, 16209579598652226016, 1054597422432310244224, -253507355147241835002176, -32440318000852390709512960, 4115817835612084772939010176
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 44/29, 254/841, -136840/24389, -7302644/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(44/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[Numerator[HermiteH[n, 22/29]], {n, 0, 15}] (* Wesley Ivan Hurt, May 24 2014 *)
Table[29^n*HermiteH[n, 22/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 22/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(44*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 22/29).
E.g.f.: exp(44*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160285 Numerator of Hermite(n, 23/29).

Original entry on oeis.org

1, 46, 434, -134780, -8389844, 520867016, 94518470776, -908740269776, -1154662527326320, -40886467186904864, 15598503848068208416, 1405241555094877399616, -223962406662593631730496, -38665666254514312493452160, 3118541336376613976720226176
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 46/29, 434/841, -134780/24389, -8389844/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(46/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],23/29]] (* Harvey P. Dale, Sep 28 2015 *)
Table[29^n*HermiteH[n, 23/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 23/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(46*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 23/29).
E.g.f.: exp(46*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160286 Numerator of Hermite(n, 24/29).

Original entry on oeis.org

1, 48, 622, -131616, -9456180, 431615808, 100244032584, 455846829696, -1158392591818608, -61736719347682560, 14572384526261325024, 1737886076688564260352, -186199726823835951097152, -44015079459426106683608064, 1958719412677543785877138560
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 48/29, 622/841, -131616/24389, -9456180/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(48/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[29^n*HermiteH[n, 24/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 24/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(48*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 24/29).
E.g.f.: exp(48*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(48/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160287 Numerator of Hermite(n, 25/29).

Original entry on oeis.org

1, 50, 818, -127300, -10492628, 331843000, 104835151480, 1892798018000, -1139689172625520, -82453948761484000, 13129917257130921760, 2043371281024706968000, -140761165040200966003520, -48281464188212733742288000, 663810425358397635518568320
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 50/29, 818/841, -127300/24389, -10492628/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(50/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],25/29]] (* Harvey P. Dale, Dec 05 2012 *)
Table[29^n*HermiteH[n, 25/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 25/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(50*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 25/29).
E.g.f.: exp(50*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160288 Numerator of Hermite(n, 26/29).

Original entry on oeis.org

1, 52, 1022, -121784, -11489780, 221894192, 108167547784, 3385356299104, -1097526180055408, -102624715723624640, 11277866096050285024, 2312596755465981266048, -88408047224891347679552, -51274671368019715953249536, -733152550517551021207891840
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 52/29, 1022/841, -121784/24389, -11489780/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(52/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],26/29]] (* Harvey P. Dale, Nov 24 2017 *)
Table[29^n*HermiteH[n, 26/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 26/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(52*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 26/29).
E.g.f.: exp(52*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160289 Numerator of Hermite(n, 27/29).

Original entry on oeis.org

1, 54, 1234, -115020, -12437844, 102210984, 110121661176, 4915056452976, -1031159390225520, -121819606703423136, 9031432087249072416, 2536703117463027057984, -30117588135278876709696, -52827165482178797480672640, -2194115753871647145822109824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 54/29, 1234/841, -115020/24389, -12437844/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(54/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],27/29]] (* Harvey P. Dale, Sep 02 2011 *)
Table[29^n*HermiteH[n, 27/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 27/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(54*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 27/29).
E.g.f.: exp(54*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(54/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160290 Numerator of Hermite(n, 28/29).

Original entry on oeis.org

1, 56, 1454, -106960, -13326644, -26665184, 110583825736, 6461799278144, -940153204639600, -139598550546523264, 6414520381228962016, 2707260761541343173376, 32925146552816962489024, -52799543003992720712035840, -3676715662747488061659005824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 56/29, 1454/841, -106960/24389, -13326644/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(56/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[29^n*HermiteH[n, 28/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 28/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(56*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 28/29).
E.g.f.: exp(56*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(56/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A165850 Totally multiplicative sequence with a(p) = 29.

Original entry on oeis.org

1, 29, 29, 841, 29, 841, 29, 24389, 841, 841, 29, 24389, 29, 841, 841, 707281, 29, 24389, 29, 24389, 841, 841, 29, 707281, 841, 841, 24389, 24389, 29, 24389, 29, 20511149, 841, 841, 841, 707281, 29, 841, 841, 707281, 29, 24389, 29, 24389, 24389
Offset: 1

Views

Author

Jaroslav Krizek, Sep 28 2009

Keywords

Links

Crossrefs

Cf. A001222, A009973.

Programs

  • Magma
    [n eq 1 select 1 else 29^(&+[p[2]: p in Factorization(n)]): n in [1..100]]; // Vincenzo Librandi, Apr 14 2016
  • Mathematica
    29^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 13 2016 *)
  • PARI
    a(n) = 29^bigomega(n); \\ Michel Marcus, Apr 14 2016

Formula

a(n) = A009973(A001222(n)) = 29^bigomega(n) = 29^A001222(n).
Previous Showing 31-40 of 41 results. Next

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

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