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.

Previous Showing 21-30 of 35 results. Next

A159519 Numerator of Hermite(n, 13/15).

Original entry on oeis.org

1, 26, 226, -17524, -760724, 11764376, 2017502776, 20691256976, -5817161063024, -225734712752224, 17690399773689376, 1475756601500931776, -49197807240738185024, -9248228636364224401024, 47353227812848547963776, 59495024332228675973509376
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 26/15, 226/225, -17524/3375, -760724/50625, 11764376/759375, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/15)^(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
  • Maple
    A159519 := proc(n)
        orthopoly[H](n,13/15) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n,13/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,13/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -26*a(n-1) + 450*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,13/15).
E.g.f.: exp(26*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159520 Numerator of Hermite(n, 14/15).

Original entry on oeis.org

1, 28, 334, -15848, -894644, 3476368, 2110287304, 49701850912, -5255753182064, -326087752380992, 12155343320691424, 1807744498693823872, -9552103473995480384, -10029279190218522359552, -224940012003245065821056, 56886138562285829022188032
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 28/15, 334/225, -15848/3375, -894644/50625, 3476368/759375

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/15)^(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
  • Maple
    A159520 := proc(n)
        orthopoly[H](n,14/15) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n,14/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
  • PARI
    a(n)=numerator(polhermite(n,14/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -28*a(n-1) +450*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,14/15).
E.g.f.: exp(28*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160291 Numerator of Hermite(n, 1/30).

Original entry on oeis.org

1, 1, -449, -1349, 604801, 3033001, -1357769249, -9546871949, 4267426262401, 38636165278801, -17244440197445249, -191107183952049749, 85168871793401932801, 1117147665134470577401, -497120752326266836308449, -7535151042673431473934749, 3348029927159627713608096001
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 1/15, -449/225, -1349/3375, 604801/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(1/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[15^n*HermiteH[n, 1/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 1/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 1/30).
E.g.f.: exp(x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160292 Numerator of Hermite(n, 7/30).

Original entry on oeis.org

1, 7, -401, -9107, 477601, 19735807, -936451601, -59841840107, 2530929662401, 233147132022007, -8618235208570001, -1109489740559021507, 34893836098508354401, 6235501451708274618607, -160480431014315950915601, -40407022162862341753633307, 800393754206596276404873601
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 7/15, -401/225, -9107/3375, 477601/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(7/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[15^n*HermiteH[n, 7/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 7/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(7*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 7/30).
E.g.f.: exp(7*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160293 Numerator of Hermite(n, 11/30).

Original entry on oeis.org

1, 11, -329, -13519, 295441, 27584051, -361317689, -78451432279, 275184965281, 285452190822491, 2025474989659351, -1262254633814956639, -23910902170778310479, 6553155098722204435331, 211963483784997365090791, -38953278800314916926586599, -1859239582352196300555291839
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 11/15, -329/225, -13519/3375, 295441/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(11/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],11/30]] (* Harvey P. Dale, Jul 24 2013 *)
Table[15^n*HermiteH[n, 11/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(11*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 11/30).
E.g.f.: exp(11*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160294 Numerator of Hermite(n, 13/30).

Original entry on oeis.org

1, 13, -281, -15353, 179761, 29972293, -14822441, -81117882833, -1007841787679, 278922434958973, 7707750894566599, -1154950195686012713, -53167719472022830319, 5545550703568171856053, 383123318057719791494839, -29956366297729125403700993
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 13/15, -281/225, -15353/3375, 179761/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(13/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Table[15^n*HermiteH[n, 13/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 13/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(13*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 13/30).
E.g.f.: exp(13*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160295 Numerator of Hermite(n, 17/30).

Original entry on oeis.org

1, 17, -161, -18037, -89279, 30948857, 727008319, -71202772477, -3500523336959, 196821084188897, 17523077945895199, -587802553769818117, -96731879246268143039, 1529691843170459400137, 591886254924566446580479, 425007721743735371005043
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 17/15, -161/225, -18037/3375, -89279/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(17/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],17/30]] (* Harvey P. Dale, Jan 02 2016 *)
Table[15^n*HermiteH[n, 17/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(17*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 17/30).
E.g.f.: exp(17*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160296 Numerator of Hermite(n, 19/30).

Original entry on oeis.org

1, 19, -89, -18791, -236879, 29323099, 1090116631, -58460151311, -4544610262559, 124108949730979, 20763741608252551, -163979183232607031, -105896125442269661039, -1126538793947045592341, 598088096752283650823671, 18460868240159776597398049
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 19/15, -89/225, -18791/3375, -236879/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(19/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],19/30]] (* Harvey P. Dale, Sep 10 2011 *)
Table[15^n*HermiteH[n, 19/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 19/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(19*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 19/30).
E.g.f.: exp(19*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160297 Numerator of Hermite(n, 23/30).

Original entry on oeis.org

1, 23, 79, -18883, -540959, 21547343, 1712746639, -18784653403, -5827198941119, -66400823394937, 22072936773448399, 806481251066529677, -90711968254039392479, -6441374025602166282817, 382513411697280621497359, 49378464830331101876186357
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 23/15, 79/225, -18883/3375, -540959/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(23/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],23/30]] (* Harvey P. Dale, Sep 30 2012 *)
Table[15^n*HermiteH[n, 23/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 23/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(23*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 23/30).
E.g.f.: exp(23*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160298 Numerator of Hermite(n, 29/30).

Original entry on oeis.org

1, 29, 391, -14761, -955919, -1151851, 2117414071, 64515005759, -4798919156639, -371422676274931, 8664364972414951, 1922668627437223079, 12868783582225461841, -10009215864276466233211, -365549644020036472532969, 52457120268360679565773199
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 29/15, 391/225, -14761/3375, -955919/50625, ...

Links

Crossrefs

Cf. A001024 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(29/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
  • Mathematica
    Table[15^n*HermiteH[n, 29/30], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 29/30)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(29*x - 225*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 15^n * Hermite(n, 29/30).
E.g.f.: exp(29*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(29/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
Previous Showing 21-30 of 35 results. Next

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

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