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 24 results. Next

A159488 Numerator of Hermite(n, 1/13).

Original entry on oeis.org

1, 2, -334, -2020, 334636, 3400312, -558734216, -8013301168, 1305938552720, 24279843463712, -3924105390446816, -89914081688240192, 14409995678304781504, 393511506684111781760, -62530497997102986365056, -1987157445623422924018432, 313055309954065295022797056
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(2/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 08 2018
  • Mathematica
    Numerator[Table[HermiteH[n,1/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,1/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 08 2018: (Start)
a(n) = 13^n * Hermite(n,1/13).
E.g.f.: exp(2*x-169*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/13)^(n-2k)/(k!*(n-2k)!). (End)

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)

A159281 Numerator of Hermite(n, 2/11).

Original entry on oeis.org

1, 4, -226, -2840, 152716, 3359984, -171346424, -5564082464, 268004512400, 11844081699904, -536337501207584, -30808027718598016, 1304498317340196544, 94684505764169424640, -3725213683295580628864, -335691960262188333195776, 12179757829314204349993216
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Comments

Denominator is 11^n. - Robert Israel, May 21 2014

Links

Crossrefs

Cf. A159280.

Programs

Formula

a(n) = 4*a(n-1) - 242*(n-1)*a(n-2) for n >= 2.
E.g.f.: exp(-11*x^2 + 4*x). - Robert Israel, May 21 2014
From G. C. Greubel, Jun 27 2018: (Start)
a(n) = 11^n * Hermite(n, 2/11).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159307 Numerator of Hermite(n, 3/11).

Original entry on oeis.org

1, 6, -206, -4140, 124716, 4755816, -122371464, -7639673616, 161459218320, 15759163430496, -257103196917984, -39679794683308224, 446329942095824064, 117908103412902026880, -696705377356050344064, -403652886627048369133824, 107123200040172534149376
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(6/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018
  • Magma
    I:=[1, 6]; [n le 2 select I[n] else 6*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jan 27 2018
  • Mathematica
    Numerator[Table[HermiteH[n,3/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,3/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 26 2018: (Start)
a(n) = 11^n * Hermite(n,6/11).
E.g.f.: exp(6*x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
a(n) = 6*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]

A159326 Numerator of Hermite(n, 4/11).

Original entry on oeis.org

1, 8, -178, -5296, 86860, 5821408, -58529336, -8920919104, 27781342352, 17493150124160, 79437437350624, -41697923801662208, -545045848640658752, 116730403930901782016, 2648557471270726689920, -374294148747729423950848, -12608616810694573276016384
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(8/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018
  • Magma
    I:=[1, 8]; [n le 2 select I[n] else 8*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jun 27 2018
  • Mathematica
    Numerator[Table[HermiteH[n,4/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,4/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 26 2018: (Start)
a(n) = 11^n * Hermite(n, 8/11).
E.g.f.: exp(8*x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
a(n) = 8*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]

A159327 Numerator of Hermite(n, 5/11).

Original entry on oeis.org

1, 10, -142, -6260, 40492, 6464600, 15650680, -9230092400, -118813175920, 16681327127200, 425588368425760, -36112927963566400, -1494045516385037120, 89931487642346454400, 5599582070970791323520, -248692059422561874272000, -22813403511849591247097600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018
  • Magma
    I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jun 27 2018
  • Mathematica
    Numerator[Table[HermiteH[n,5/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
Table[11^n*HermiteH[n,5/11], {n,0,30}] (* G. C. Greubel, Jun 26 2018 *)
RecurrenceTable[{a[n] == 10*a[n-1] - 242*(n-1)*a[n-2], a[0]==1, a[1]==10}, a,{n,0,30}] (* Georg Fischer, Dec 23 2019 *)
  • PARI
    a(n)=numerator(polhermite(n,5/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 26 2018: (Start)
a(n) = 11^n * Hermite(n,5/11).
E.g.f.: exp(10*x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
a(n) = 10*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]

A159449 Numerator of Hermite(n, 6/11).

Original entry on oeis.org

1, 12, -98, -6984, -12660, 6608592, 94621704, -8460215136, -261811748208, 13237235524800, 729072813894624, -23285236203280512, -2220214665026855232, 40977749954004344064, 7476528335622538688640, -49114276816696253425152, -27729169180110170480865024
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(12/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n,6/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,6/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 11^n * Hermite(n,6/11).
E.g.f.: exp(12*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159450 Numerator of Hermite(n, 7/11).

Original entry on oeis.org

1, 14, -46, -7420, -70484, 6195784, 172026616, -6587905744, -383643767920, 7383172769504, 938940545302816, -4722110467960256, -2565569278147539776, -22204961095108973440, 7760411493720634507136, 183876169102318085114624, -25596027354773450069298944
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n,7/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,7/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 11^n * Hermite(n,7/11).
E.g.f.: exp(14*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159454 Numerator of Hermite(n, 8/11).

Original entry on oeis.org

1, 16, 14, -7520, -130484, 5191616, 240951496, -3683002496, -467099874160, -343305154304, 1011850643451616, 17020408768641536, -2421219872569937216, -88166785025254016000, 6206489158700958225536, 398012894204775937816576, -16161349338808063353630464
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(16/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n,8/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,8/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 11^n * Hermite(n,8/11).
E.g.f.: exp(16*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159472 Numerator of Hermite(n, 1/12).

Original entry on oeis.org

1, 1, -71, -215, 15121, 77041, -5366519, -38648231, 2666077345, 24927458401, -1702690661159, -19650460709879, 1328880542928049, 18306878596263505, -1225525309584390359, -19678858934618003399, 1303888475416523584321, 23973933968096463499969
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Links

Crossrefs

Cf. A159280.

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(1/6)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n,1/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,1/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 6^n * Hermite(n,1/12).
E.g.f.: exp(x-36*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/6)^(n-2*k)/(k!*(n-2*k)!)). (End)
Showing 1-10 of 24 results. Next

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

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