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 1-7 of 7 results.

A159529 Numerator of Hermite(n, 1/17).

Original entry on oeis.org

1, 2, -574, -3460, 988396, 9976312, -2836511816, -40270873648, 11395985060240, 209004489868832, -58863905303630816, -1325773762049110592, 371605162396386506944, 9938777138365404080000, -2772363635969717405017216, -85969311875592284625394432, 23864454100106265332248473856
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(2/17)^(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,1/17],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,1/17)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 17^n * Hermite(n,1/17).
E.g.f.: exp(2*x-289*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/17)^(n-2k)/(k!*(n-2k)!). (End)

A159530 Numerator of Hermite(n, 2/17).

Original entry on oeis.org

1, 4, -562, -6872, 947020, 19676144, -2658183224, -78869600288, 10439530923152, 406451155424320, -52680635240539424, -2560010219314727296, 324703437982090748608, 19055044633095311519488, -2363601454465048638962560, -163647826988867455371547136
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

The denominators are the powers of 17, A001026.
Cf. A159521, A159529.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/17)^(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,2/17],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    /* needs version >= 2.4 */
A159530(n)=numerator(polhermite(n,2/17)); /* Joerg Arndt, Apr 30 2011 */

Formula

From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 17^n * Hermite(n,2/17).
E.g.f.: exp(4*x-289*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159522 Numerator of Hermite(n, 3/16).

Original entry on oeis.org

1, 3, -119, -1125, 42321, 702963, -24976551, -614805237, 20534573985, 691164284643, -21582336376791, -949437293473413, 27539617738101489, 1540954535989466835, -41203060308232477191, -2884999709417821999893, 70454876663552890207041
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(3/8)^(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,3/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,3/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 16^n * Hermite(n,3/16).
E.g.f.: exp(6*x-252*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/8)^(n-2k)/(k!*(n-2k)!). (End)

A159526 Numerator of Hermite(n, 11/16).

Original entry on oeis.org

1, 11, -7, -2893, -29135, 1160731, 31414441, -545882557, -34152047263, 183311218475, 41359581850201, 220317040704211, -55810803797336687, -952325816292371653, 82393593539552158985, 2612897391731003751011, -129453828286899103990079
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(11/8)^(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,11/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,11/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 8^n * Hermite(n, 11/16).
E.g.f.: exp(11*x-64*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/8)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159527 Numerator of Hermite(n, 13/16).

Original entry on oeis.org

1, 13, 41, -2795, -52079, 754013, 43132729, -18356507, -38885559775, -486715213907, 38468867080009, 1123090745841077, -39563985152718671, -2239399192597236995, 36722281790359787609, 4490393016408925933957, -12131671824174755067839
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(13/8)^(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,13/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,13/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 16^n * Hermite(n,13/16).
E.g.f.: exp(26*x-252*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/8)^(n-2k)/(k!*(n-2k)!). (End)

A159528 Numerator of Hermite(n, 15/16).

Original entry on oeis.org

1, 15, 97, -2385, -73023, 125775, 48621345, 632724975, -34073850495, -1159018131825, 21867803792865, 1811560265628975, -3616463755919295, -2836803524344895025, -36534257175323718495, 4535538057996196107375, 138178844646564481121025
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(15/8)^(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,15/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,15/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 8^n * Hermite(n, 15/16).
E.g.f.: exp(15*x-64*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/8)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159531 Numerator of Hermite(n, 3/17).

Original entry on oeis.org

1, 6, -542, -10188, 878700, 28826856, -2366481864, -114170427792, 8889763054992, 581262636440160, -42756971593427424, -3616239868184689344, 250151386181903425728, 26583148042820425844352, -1720138627513899785854080, -225431665727586284647620864
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159521, A159529, A159530.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(6/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/17],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
Table[17^n*HermiteH[n, 3/17], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,3/17)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 09 2018: (Start)
a(n) = 17^n * Hermite(n, 3/17).
E.g.f.: exp(6*x-289*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/17)^(n-2*k)/(k!*(n-2*k)!)). (End)
Showing 1-7 of 7 results.

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

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