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 41 results. Next

A160253 Numerator of Hermite(n, 10/29).

Original entry on oeis.org

1, 20, -1282, -92920, 4610572, 717377200, -24427366520, -7728318032800, 133041452750480, 106653076504366400, 119080018350561760, -1791523146436431612800, -38033681428250725939520, 35399429559107921153964800, 1539633069292288796472840320
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 20/29, -1282/841, -92920/24389, 4610572/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[29^n*HermiteH[n, 10/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 10/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(20*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 29^n * Hermite(n, 10/29).
E.g.f.: exp(20*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160259 Numerator of Hermite(n, 11/29).

Original entry on oeis.org

1, 22, -1198, -100364, 3837100, 759665192, -15557376776, -8008803406736, 6978879212432, 107919993983713120, 2268593594123893024, -1765305239735329031872, -80810233952657507431232, 33853095811859416015817344, 2511764683469716209839300480
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 22/29, -1198/841, -100364/24389, 3837100/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[29^n*HermiteH[n, 11/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0,20],11/29]//Numerator (* Harvey P. Dale, Mar 18 2023 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(22*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 29^n * Hermite(n, 11/29).
E.g.f.: exp(22*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160260 Numerator of Hermite(n, 12/29).

Original entry on oeis.org

1, 24, -1106, -107280, 3006156, 793927584, -6227509944, -8161777416384, -122559955912560, 106883437972961664, 4420515123955413216, -1691687063730285271296, -122388860352949901833536, 31207679045861280271833600, 3425139117578273280016104576
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 24/29, -1106/841, -107280/24389, 3006156/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(24/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Table[29^n*HermiteH[n, 12/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0,20],12/29]//Numerator (* Harvey P. Dale, Dec 27 2019 *)
  • PARI
    a(n)=numerator(polhermite(n, 12/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(24*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 29^n * Hermite(n, 12/29).
E.g.f.: exp(24*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160261 Numerator of Hermite(n, 13/29).

Original entry on oeis.org

1, 26, -1006, -113620, 2122156, 819611416, 3462564856, -8181491724016, -253487023438960, 103499490028946336, 6528273301571581216, -1571126316446016259904, -161635396853273818415936, 27509093252961272911088000, 4249556012170678409171144576
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 26/29, -1006/841, -113620/24389, 2122156/707281, 819611416/20511149,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018
  • Maple
    A160261 := proc(n)
        orthopoly[H](n,13/29) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[HermiteH[Range[0,20],13/29]] (* Harvey P. Dale, May 15 2012 *)
Table[29^n*HermiteH[n, 13/29], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,13/29)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -26*a(n-1) +1682*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 12 2018: (Start)
a(n) = 29^n * Hermite(n, 13/29).
E.g.f.: exp(26*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160263 Numerator of Hermite(n, 14/29).

Original entry on oeis.org

1, 28, -898, -119336, 1189900, 836209808, 13406815624, -8063638544864, -383633726413168, 97762575920121280, 8544799476205933024, -1405112141642673804928, -197439019874757039348032, 22832490910422530976921856, 4956511354073268289737879680
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 28/29, -898/841, -119336/24389, 1189900/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Maple
    seq(coeff(series(factorial(n)*exp(28*x-841*x^2),x,n+1), x, n), n = 0..15); # Muniru A Asiru, Sep 28 2018
  • Mathematica
    Table[29^n*HermiteH[n, 14/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 14/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(28*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 29^n * Hermite(n, 14/29).
E.g.f.: exp(28*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160269 Numerator of Hermite(n, 15/29).

Original entry on oeis.org

1, 30, -782, -124380, 214572, 843265800, 23493423480, -7805435749200, -510774640529520, 89706704225349600, 10423307635096361760, -1196167536017489419200, -228737063945077567859520, 17281333628624679401347200, 5520004649081806480856680320
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 30/29, -782/841, -124380/24389, 214572/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(30/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],15/29]] (* Harvey P. Dale, Dec 12 2012 *)
Table[29^n*HermiteH[n, 15/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 15/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(30*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)
a(n) = 29^n * Hermite(n, 15/29).
E.g.f.: exp(30*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160270 Numerator of Hermite(n, 16/29).

Original entry on oeis.org

1, 32, -658, -128704, -798260, 840376192, 33605404744, -7405703577856, -632652549947248, 79406265745318400, 12118094804951629024, -947834356077803359232, -254539689475704747697472, 10985818579851831076419584, 5917311044631018607598349440
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 32/29, -658/841, -128704/24389, -798260/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(32/29)^(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],16/29] (* Harvey P. Dale, Jun 07 2011 *)
Table[29^n*HermiteH[n, 16/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 16/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(32*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 16/29).
E.g.f.: exp(32*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160279 Numerator of Hermite(n, 17/29).

Original entry on oeis.org

1, 34, -526, -132260, -1842644, 827195384, 43621279096, -6864932326064, -747004639162480, 66976371647992864, 13585352863673379616, -664640573754345065536, -273953978191332601883456, 4100670082152392338741120, 6129700469924860012300846976
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 34/29, -526/841, -132260/24389, -1842644/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(34/29)^(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],17/29]] (* Harvey P. Dale, Dec 24 2015 *)
Table[29^n*HermiteH[n, 17/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 17/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(34*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 17/29).
E.g.f.: exp(34*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160280 Numerator of Hermite(n, 18/29).

Original entry on oeis.org

1, 36, -386, -135000, -2912244, 803439216, 53415783816, -6185340350496, -851589691267440, 52572710870646336, 14783982337749774816, -352049632685279478144, -286207027989716394858816, -3197683221510109228058880, 6143086278048774757772750976
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 36/29, -386/841, -135000/24389, -2912244/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(36/29)^(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[29^n*HermiteH[n, 18/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 18/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(36*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 18/29).
E.g.f.: exp(36*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160281 Numerator of Hermite(n, 19/29).

Original entry on oeis.org

1, 38, -238, -136876, -4000340, 768888808, 62860634104, -5370921754384, -944216132607088, 36390910087921760, 15676398398747125024, -16391968526453252288, -290667617977624530780992, -10714513990411799725496704, 5948586603063089600488296320
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 38/29, -238/841, -136876/24389, -4000340/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(38/29)^(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[29^n*HermiteH[n, 19/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 19/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(38*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 19/29).
E.g.f.: exp(38*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
Previous Showing 21-30 of 41 results. Next

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

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