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.

A159521 Numerator of Hermite(n, 1/16).

Original entry on oeis.org

1, 1, -127, -383, 48385, 244481, -30721919, -218483327, 27308356097, 251035282945, -31208190940799, -352533353110399, 43588599491534593, 585079829869107457, -71946349724044455295, -1120409404849485018239, 137016582065315869148161
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159513.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(1/8)^(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,1/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,1/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 8^n * Hermite(n,1/16).
E.g.f.: exp(2*x-64*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/8)^(n-2k)/(k!*(n-2k)!). (End)

A159514 Numerator of Hermite(n, 2/15).

Original entry on oeis.org

1, 4, -434, -5336, 564556, 11863024, -1222798904, -36921360416, 3704131105936, 147733421921344, -14410797291355424, -722443587811469696, 68443672240963470016, 4174970063145790238464, -383695602357053138639744, -27837093807246691056882176, 2478596940681121921590743296
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159513.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/15)^(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,2/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,2/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,2/15).
E.g.f.: exp(4*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159515 Numerator of Hermite(n, 4/15).

Original entry on oeis.org

1, 8, -386, -10288, 438796, 22028768, -811060856, -65966160448, 2027112412816, 253695076915328, -6180244656582176, -1191069803371633408, 21063652623108703936, 6600286159191690034688, -70420078571652397748096, -42145163431480866400519168, 138174222906806753595494656
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159513, A159514.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(8/15)^(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,4/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,4/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,4/15).
E.g.f.: exp(8*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159516 Numerator of Hermite(n, 7/15).

Original entry on oeis.org

1, 14, -254, -16156, 116716, 30714824, 167396536, -80586473296, -1655509714544, 266934167861984, 10441892693970976, -1055017257663334336, -66457610442443011904, 4766686645187803247744, 455510634120920865106816, -23652976986990268349291776
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159513, A159514, A159515.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/15)^(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,7/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,7/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,7/15).
E.g.f.: exp(14*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159518 Numerator of Hermite(n, 11/15).

Original entry on oeis.org

1, 22, 34, -19052, -465044, 24062632, 1575726904, -30303114512, -5630208266864, -14773369627808, 22477329348987424, 560981409002859328, -98921189279424843584, -5205565772762786930048, 464166510283854022505344, 43006727594650346154419968
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159513, A159514.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/15)^(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,11/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,11/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,11/15).
E.g.f.: exp(22*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/15)^(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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