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 1-3 of 3 results.

A159249 Numerator of Hermite(n, 3/10).

Original entry on oeis.org

1, 3, -41, -423, 4881, 99243, -922521, -32540463, 225260961, 13691968083, -60291528201, -7026858626103, 12079764632241, 4252354469558523, 4905216397718919, -2961932479497809343, -12564709736782617279, 2331851854387899622563, 17675558839428923554839
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159247.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(3/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/10],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,3/10)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 5^n * Hermite(n, 3/10).
E.g.f.: exp(3*x-25*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159252 Numerator of Hermite(n, 7/10).

Original entry on oeis.org

1, 7, -1, -707, -4799, 107807, 1954399, -18661307, -814668799, 1761841207, 378933847999, 1771616332493, -196012302071999, -2435055913999793, 110362604948800799, 2477077374441460693, -65432412090510374399, -2439688784186741175193
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159247.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(7/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018
  • Mathematica
    Numerator[Table[HermiteH[n,7/10],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,7/10)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)
a(n) = 5^n * Hermite(n, 7/10).
E.g.f.: exp(7*x-25*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159279 Numerator of Hermite(n, 9/10).

Original entry on oeis.org

1, 9, 31, -621, -10239, 32049, 2848191, 16019019, -852695679, -14081868711, 256976237151, 9353720489859, -57153446024319, -6126613308134271, -17989779857401089, 4126721296977379899, 50632826565847235841, -2845681598489278796631
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159247.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(9/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 27 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/10],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
Table[5^n*HermiteH[n, 9/10], {n,0,30}] (* G. C. Greubel, Jun 27 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,9/10)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 27 2018: (Start)
a(n) = 5^n * Hermite(n, 9/10).
E.g.f.: exp(9*x - 25*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
Showing 1-3 of 3 results.

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

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