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 24 results. Next

A159480 Numerator of Hermite(n, 5/12).

Original entry on oeis.org

1, 5, -47, -955, 5377, 301925, -426095, -132562075, -448058495, 74115462725, 660919218385, -50058537070075, -773740706311295, 39381872496988325, 921130663592313745, -35091274159002662875, -1170277487474712158975, 34573760393797506837125
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(5/6)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,5/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,5/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 6^n * Hermite(n,5/12).
E.g.f.: exp(5*x-36*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/6)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159485 Numerator of Hermite(n, 7/12).

Original entry on oeis.org

1, 7, -23, -1169, -3215, 314167, 3356569, -112224161, -2477279903, 47300157415, 1936378479049, -20501463985457, -1677122003305007, 5973410860299799, 1611600071115585145, 5260002350626898623, -1703708060350443666239, -17985479130375292877369
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(7/6)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,7/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,7/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 6^n * Hermite(n,7/12).
E.g.f.: exp(7*x-36*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/6)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159486 Numerator of Hermite(n, 11/12).

Original entry on oeis.org

1, 11, 49, -1045, -22079, 58091, 8587441, 69366539, -3565038335, -79170548149, 1439268811441, 72834751593131, -338718631136831, -66655130318970325, -416165794764599759, 62610547619111490251, 1138175082155994132481, -59607424953500501311861
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(11/6)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,11/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,11/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 6^n * Hermite(n,11/12).
E.g.f.: exp(11*x-36*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/6)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159492 Numerator of Hermite(n, 2/13).

Original entry on oeis.org

1, 4, -322, -3992, 310540, 6639344, -498255224, -15457610528, 1117041417872, 46265544539200, -3212977815009824, -169229451802535296, 11268933708996384448, 731470391347068698368, -46589813151941838471040, -3647677144462096434561536, 221619644102496735309926656
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,2/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,2/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n, 2/13).
E.g.f.: exp(4*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159494 Numerator of Hermite(n, 3/13).

Original entry on oeis.org

1, 6, -302, -5868, 271020, 9559656, -400665864, -21790977552, 817229568912, 63826180714080, -2103055264345824, -228350822399665344, 6449054538439781568, 964885262883681324672, -22547834064602312261760, -4701124068353193901918464, 86110774297414559755612416
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(6/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,3/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,3/13).
E.g.f.: exp(6*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159496 Numerator of Hermite(n, 4/13).

Original entry on oeis.org

1, 8, -274, -7600, 217036, 12011488, -270698936, -26524889152, 428274569360, 75149496821888, -701615265418016, -259618221381325568, 531659785773578944, 1057264784208845135360, 6122005174981655202944, -4954000917476401938899968, -70670573576968207390125824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(8/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,4/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,4/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,4/13).
E.g.f.: exp(8*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159497 Numerator of Hermite(n, 5/13).

Original entry on oeis.org

1, 10, -238, -9140, 149932, 13856600, -114819080, -29249375600, -20831812720, 78881993495200, 852190309246240, -258099234921313600, -5749435918990656320, 989356137650941398400, 35156582804554357854080, -4330067415318711118688000, -221544548972277705507065600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,5/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,5/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,5/13).
E.g.f.: exp(10*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159498 Numerator of Hermite(n, 6/13).

Original entry on oeis.org

1, 12, -194, -10440, 71436, 14972112, 58938504, -29656181088, -495322673520, 74246441579712, 2397728871804384, -222180226077773952, -11580918658301987136, 762191973071827303680, 60032860261440859119744, -2886298093438596491576832, -339002178646768313636024064
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(12/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,6/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,6/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,6/13).
E.g.f.: exp(12*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159500 Numerator of Hermite(n, 7/13).

Original entry on oeis.org

1, 14, -142, -11452, -16340, 15254344, 241175416, -27559353808, -956451987568, 61130164870880, 3765349254374176, -153905067702335936, -16154239475595889472, 398079601942332103808, 76554842682960987793280, -811944878829661686113536, -399500280706227471717519104
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,7/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,7/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,7/13).
E.g.f.: exp(14*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159501 Numerator of Hermite(n, 8/13).

Original entry on oeis.org

1, 16, -82, -12128, -110900, 14622656, 421383496, -22912610432, -1363595118448, 40138176712960, 4790267177726176, -59022762446185984, -18754577565924898112, -60676916573068018688, 81436783159504914005120, 1590111699775836488513536, -387442703422276530189741824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(16/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018
  • Mathematica
    Numerator[Table[HermiteH[n,8/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,8/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)
a(n) = 13^n * Hermite(n,8/13).
E.g.f.: exp(16*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
Previous Showing 11-20 of 24 results. Next

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

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