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.

Showing 1-10 of 12 results. Next

A159507 Numerator of Hermite(n, 1/14).

Original entry on oeis.org

1, 1, -97, -293, 28225, 143081, -13687169, -97818797, 9291579137, 85981515985, -8109191282849, -92371076948149, 8649337125963073, 117277723616986297, -10901977774859968705, -171807014577365168189, 15854100314466788828161, 285247499171775372548513
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			G.f. = 1 + x - 97*x^2 - 293*x^3 + 28225*x^4 + 143081*x^5 - 13687169*x^6 + ...

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(1/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 1/14], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
a[ n_] := If[ n < 0, 0, HermiteH[n, 1/14] 7^n]; (* Michael Somos, Jan 24 2014 *)
a[ n_] := Sum[(-49)^k n! / (k! (n - 2 k)!), {k, 0, n/2}]; (* Michael Somos, Jan 24 2014 *)
  • PARI
    {a(n) = if( n<0, 0, sum(k=0, n\2, (-49)^k * n! / (k! * (n - 2*k)!)))}; \\ Michael Somos, Jan 24 2014

Formula

a(n) = Sum_{k = 0..n/2} (-49)^k * n! / (k! * (n - 2*k)!). - Michael Somos, Jan 24 2014
0 = a(n) * (-98*a(n+1) + a(n+2) - a(n+3)) + a(n+1) * (-a(n+1) + a(n+2)) for all n in Z. - Michael Somos, Jan 24 2014
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 7^n * Hermite(n,1/14).
E.g.f.: exp(x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/7)^(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)

A159502 Numerator of Hermite(n, 9/13).

Original entry on oeis.org

1, 18, -14, -12420, -209364, 13023288, 588244344, -15822829872, -1676597055600, 12606184973088, 5327119572650784, 53279247098676672, -18847204123339434816, -555350300452342408320, 72818309509811313231744, 3938647192917087914341632, -298293179742235775626792704
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(18/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018
  • Mathematica
    Numerator[Table[HermiteH[n,9/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,9/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 13^n * Hermite(n,9/13).
E.g.f.: exp(18*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159504 Numerator of Hermite(n, 10/13).

Original entry on oeis.org

1, 20, 62, -12280, -308468, 10433200, 729974920, -6559031200, -1858301284720, -19430405329600, 5264344401526240, 170961658044572800, -16153599323983104320, -1016492471508449363200, 50649065999412773118080, 5823023695166237849024000, -140330290713698002728185600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280, A159488.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018
  • Mathematica
    Numerator[Table[HermiteH[n,10/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,10/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 13^n * Hermite(n,10/13).
E.g.f.: exp(20*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
Showing 1-10 of 12 results. Next

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

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