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 1-5 of 5 results.

A159508 Numerator of Hermite(n, 3/14).

Original entry on oeis.org

1, 3, -89, -855, 23601, 405963, -10346601, -269746047, 6288530145, 230346491283, -4855444114041, -240305893799463, 4513251073537809, 296139484328781915, -4861463414700822921, -420887762743191256143, 5883687931380635925441, 677603075775465797408547
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159507.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(3/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,3/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 7^n * Hermite(n,3/14).
E.g.f.: exp(3*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159509 Numerator of Hermite(n, 5/14).

Original entry on oeis.org

1, 5, -73, -1345, 14737, 600925, -4216505, -374426425, 1020390305, 298652268725, 593277094615, -289712837877425, -2088116897382095, 330261712856941325, 4311569491549495655, -431561222581976019625, -8495813265487638710975, 634208930681100205217125
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159507.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(5/7)^(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,5/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,5/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 7^n * Hermite(n,5/14).
E.g.f.: exp(5*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159512 Numerator of Hermite(n, 13/14).

Original entry on oeis.org

1, 13, 71, -1625, -41999, 91013, 21762679, 229399183, -11947008415, -335160068867, 6180180526759, 408799214337527, -1347844821458351, -498269858739890315, -4760353861080634921, 621741645997081258207, 15080361573750589690561
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159507, A159508, A159509.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(13/7)^(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,13/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,13/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 7^n * Hermite(n,13/14).
E.g.f.: exp(13*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159510 Numerator of Hermite(n, 9/14).

Original entry on oeis.org

1, 9, -17, -1917, -12255, 641169, 11775471, -271028133, -10517226303, 117831019545, 10336672775151, -22444344177741, -11344932349212447, -75709842389888607, 13772055231387660015, 227822400841416108939, -18194519582567115241599
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159507, A159508, A159509.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(9/7)^(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,9/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
With[{nn=20},CoefficientList[Series[Exp[9x-49x^2],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 11 2021 *)
  • PARI
    a(n)=numerator(polhermite(n,9/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 7^n * Hermite(n,9/14).
E.g.f.: exp(9*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159511 Numerator of Hermite(n, 11/14).

Original entry on oeis.org

1, 11, 23, -1903, -27695, 441331, 18425191, -56825527, -13264761823, -101361166885, 10584547092151, 215763961560961, -9036738188168207, -353142538865540413, 7628236524205351175, 568422165089780309561, -4960863874594282822079
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159507, A159508, A159509.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(11/7)^(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,11/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,11/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 7^n * Hermite(n,11/14).
E.g.f.: exp(11*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
Showing 1-5 of 5 results.

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

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