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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A160307 Numerator of Hermite(n, 9/31).

Original entry on oeis.org

1, 18, -1598, -97956, 7450860, 887201208, -55633142856, -11232600902064, 546301487747472, 182545898249590560, -6164096966563140576, -3619485909755267093568, 65170591691483110373568, 84652893673042176232776576, -104600317888637823603991680
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 18/31, -1598/961, -97956/29791, 7450860/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(18/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],9/31]] (* Harvey P. Dale, Jan 18 2017 *)
Table[31^n*HermiteH[n, 9/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • Maxima
    makelist(num(hermite(n, 9/31)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */
  • PARI
    a(n)=numerator(polhermite(n, 9/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(18*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
  • Sage
    [numerator(hermite(n, 9/31)) for n in range(20)] # Bruno Berselli, Jan 19 2017

Formula

From Vincenzo Librandi, Jan 19 2017: (Start)
E.g.f.: exp(18*x - 961*x^2).
a(n+2) = -1922*(n+1)*a(n)+18*a(n+1). (End)
From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 9/31).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160308 Numerator of Hermite(n, 10/31).

Original entry on oeis.org

1, 20, -1522, -107320, 6629452, 957665200, -44555729720, -11934909680800, 360754594036880, 190726263132718400, -2425807704995582240, -3714274931510759292800, -22999072131198586137920, 85206055577740180606380800, 2278775927824931485369685120
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 20/31, -1522/961, -107320/29791, 6629452/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 10/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 10/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(20*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 10/31).
a(n+2) = 20*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(20*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160309 Numerator of Hermite(n, 11/31).

Original entry on oeis.org

1, 22, -1438, -116204, 5735020, 1019546792, -32683512776, -12476450886416, 165242061387152, 195473234180049760, 1442053974086139424, -3725270373510661319872, -112443853337363708739392, 83445871121227891089261184, 4645331284154383230526194560
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 22/31, -1438/961, -116204/29791, 5735020/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 11/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(22*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 11/31).
a(n+2) = 22*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(22*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160310 Numerator of Hermite(n, 12/31).

Original entry on oeis.org

1, 24, -1346, -124560, 4771596, 1072135584, -20123783544, -12846838359744, -37578736832880, 196631096935434624, 5369183316185589216, -3650389283510599332096, -201124616475050111174976, 79365587639487260327262720, 6930073770593296325672255616
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 24/31, -1346/961, -124560/29791, 4771596/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(24/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Numerator/@HermiteH[Range[0,20],12/31] (* Harvey P. Dale, Jul 19 2011 *)
Table[31^n*HermiteH[n, 12/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 12/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(24*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 12/31).
a(n+2) = 24*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(24*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160311 Numerator of Hermite(n, 13/31).

Original entry on oeis.org

1, 26, -1246, -132340, 3743596, 1114763416, -6992108744, -13037246540656, -244896579015280, 194093391754729376, 9282649209429277216, -3489126110080737399104, -286971048447852951277376, 73011957343257950639722880, 9068569507442760557249311616
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 26/31, -1246/961, -132340/29791, 3743596/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],13/31]] (* Harvey P. Dale, Jan 10 2015 *)
Table[31^n*HermiteH[n, 13/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 13/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(26*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 13/31).
a(n+2) = 26*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(26*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160312 Numerator of Hermite(n, 14/31).

Original entry on oeis.org

1, 28, -1138, -139496, 2655820, 1146808208, 6588199624, -13040522665184, -453772272366448, 187805452873608640, 13107905447855859424, -3242599451690793996928, -367920121625910811856192, 64485550348270970013174016, 10998447568696594705407685760
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 28/31, -1138/961, -139496/29791, 2655820/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 14/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 14/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(28*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 14/31).
a(n+2) = 28*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(28*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160313 Numerator of Hermite(n, 15/31).

Original entry on oeis.org

1, 30, -1022, -145980, 1513452, 1167697800, 20486660280, -12851291221200, -661166264043120, 177766465895877600, 16769848012294217760, -2913576034149940939200, -441955407700422580057920, 53940055420621560419971200, 12660899479421405397926325120
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 30/31, -1022/961, -145980/29791, 1513452/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(30/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 15/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 15/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(30*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 15/31).
a(n+2) = 30*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(30*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160314 Numerator of Hermite(n, 16/31).

Original entry on oeis.org

1, 32, -898, -151744, 322060, 1176913792, 34566244744, -12466050017536, -863967857346928, 164031013634531840, 20193908432692179424, -2506471012209552223232, -507146684474683728525632, 41580553522411233163802624, 14002144771001607102183125120
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 32/31, -898/961, -151744/29791, 322060/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(32/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 16/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 16/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(32*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 16/31).
a(n+2) = 32*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(32*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160315 Numerator of Hermite(n, 17/31).

Original entry on oeis.org

1, 34, -766, -156740, -912404, 1173995384, 48684045496, -11883257221424, -1059025893631600, 146710082653141024, 23307172718246211616, -2027323916172999286336, -561689258759043381720896, 27660764004806580561543040, 14974833795516881674770770816
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 34/31, -766/961, -156740/29791, -912404/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(34/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],17/31]] (* Harvey P. Dale, Feb 24 2013 *)
Table[31^n*HermiteH[n, 17/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(34*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 17/31).
a(n+2) = 34*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(34*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160316 Numerator of Hermite(n, 18/31).

Original entry on oeis.org

1, 36, -626, -160920, -2183604, 1158543216, 62691990216, -11103408719136, -1243180750254960, 125971505456256576, 26039514814335534816, -1483749801553172137344, -603942415060596074024256, 12479278480840903510828800, 15539359208014326031959897216
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 36/31, -626/961, -160920/29791, -2183604/923521, ...

Links

Crossrefs

Cf. A009975 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(36/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[31^n*HermiteH[n, 18/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 18/31)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(36*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 18/31).
a(n+2) = 36*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(36*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
Previous Showing 21-30 of 44 results. Next

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

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