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.

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A086874 Seventh power of odd primes.

Original entry on oeis.org

2187, 78125, 823543, 19487171, 62748517, 410338673, 893871739, 3404825447, 17249876309, 27512614111, 94931877133, 194754273881, 271818611107, 506623120463, 1174711139837, 2488651484819, 3142742836021, 6060711605323
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Sep 16 2003

Keywords

Crossrefs

Cf. A000040, A001248, A030078, A030514, A050997, A030516, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.

Programs

A160224 Numerator of Hermite(n, 1/29).

Original entry on oeis.org

1, 2, -1678, -10084, 8447020, 84739192, -70869959816, -996927845296, 832429051182992, 15079519188668960, -12571151938430794976, -278779816630273497152, 232033893531586021651648, 6090959605928612309819264, -5061471196749802724815296640
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 2/29, -1678/841, -10084/24389, 8447020/707281..

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(2/29)^(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, 2/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 1/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(2*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, 1/29).
E.g.f.: exp(2*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160225 Numerator of Hermite(n, 2/29).

Original entry on oeis.org

1, 4, -1666, -20120, 8326156, 168671984, -69348284024, -1979630798624, 808588172904080, 29872264717900864, -12120918702550359584, -550935167365293970816, 222057497165125577139904, 12008305406761595815509760, -4807476011385589486479101824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 4/29, -1666/841, -20120/24389, 8326156/707281

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(4/29)^(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
  • Mathematica
    Table[Numerator[HermiteH[n, 2/29]], {n, 0, 15}] (* Wesley Ivan Hurt, Feb 25 2014 *)
Table[29^n*HermiteH[n, 2/29], {n,0,30}] (* G. C. Greubel, Jul 12 2018~ *)
  • PARI
    a(n)=numerator(polhermite(n,2/29)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)
a(n) = 29^n * Hermite(n, 2/29).
E.g.f.: exp(4*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160226 Numerator of Hermite(n, 3/29).

Original entry on oeis.org

1, 6, -1646, -30060, 8125356, 250995816, -66828269064, -2934019389456, 769231923622800, 44095556446256736, -11380059521124405984, -809967616552784735424, 205694055560527051103424, 17582550705864569406418560, -4392210914651297082988957824
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 6/29, -1646/841, -30060/24389, 8125356/707281

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(6/29)^(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
    HermiteH[Range[0,20],3/29]//Numerator (* Harvey P. Dale, Mar 31 2018 *)
Table[29^n*HermiteH[n, 3/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 3/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(6*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, 3/29).
E.g.f.: exp(6*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160231 Numerator of Hermite(n, 4/29).

Original entry on oeis.org

1, 8, -1618, -39856, 7845580, 330915808, -63334001336, -3846274345024, 714924336969872, 57474862282401920, -10362725714790706976, -1049628989308325950208, 183334119260591052868288, 22652384474283979401944576, -3827564775957812126802428800
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 8/29, -1618/841, -39856/24389, 7845580/707281.

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(8/29)^(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[Numerator[HermiteH[n, 4/29]], {n, 0, 15}] (* Wesley Ivan Hurt, Jun 06 2014 *)
Table[29^n*HermiteH[n, 4/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 4/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(8*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, 4/29).
E.g.f.: exp(8*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160236 Numerator of Hermite(n, 5/29).

Original entry on oeis.org

1, 10, -1582, -49460, 7488172, 407648600, -58899040520, -4702980076400, 646447502318480, 69747774931223200, -9088444540784918240, -1264042019751023406400, 155513980696092323212480, 27068563933615579666902400, -3129783062564598942695063680
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 10/29, -1582/841, -49460/24389, 7488172/707281

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/29)^(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],5/29]] (* Harvey P. Dale, Mar 10 2013 *)
Table[29^n*HermiteH[n, 5/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 5/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(10*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, 5/29).
E.g.f.: exp(10*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160237 Numerator of Hermite(n, 6/29).

Original entry on oeis.org

1, 12, -1538, -58824, 7054860, 480426192, -53566258296, -5491256229216, 564794050426512, 80667872425448640, -7581837866251154976, -1447815668591059984512, 122905376178286149551808, 30697575968981388522011904, -2319078043886628283835690880
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 12/29, -1538/841, -58824/24389, 7054860/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(12/29)^(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, 6/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 6/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(12*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, 6/29).
E.g.f.: exp(12*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160246 Numerator of Hermite(n, 7/29).

Original entry on oeis.org

1, 14, -1486, -67900, 6547756, 548499784, -47387630984, -6198886653904, 471157554050960, 90008424571645664, -5872265109220393184, -1596153412824165573056, 86302501271257396667584, 33424995502240561479908480, -1419140555765946374814673024
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 14/29, -1486/841, -67900/24389, 6547756/707281,...

Links

Crossrefs

Cf. A009973 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(14/29)^(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, 7/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 7/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(14*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, 7/29).
E.g.f.: exp(14*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160251 Numerator of Hermite(n, 8/29).

Original entry on oeis.org

1, 16, -1426, -76640, 5969356, 611143616, -40423986104, -6814445150336, 366920889983120, 97565908182651136, -3993393901642052384, -1704952878058464945664, 46606527919245814078144, 35158473337439989488532480, -456562766083189138816177024
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 16/29, -1426/841, -76640/24389, 5969356/707281, ...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • GAP
    List(List([0..15],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(16/29)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # Muniru A Asiru, Jul 12 2018
  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(16/29)^(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
  • Mathematica
    Numerator[HermiteH[Range[0,20],8/29]] (* Harvey P. Dale, Jul 22 2014 *)
Table[29^n*HermiteH[n, 8/29], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Exp[ 16 x - 841 x^2], {x, 0, n}]]; (* Michael Somos, Jul 30 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,8/29)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)
a(n) = 29^n * Hermite(n, 8/29).
E.g.f.: exp(16*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

A160252 Numerator of Hermite(n, 9/29).

Original entry on oeis.org

1, 18, -1358, -84996, 5322540, 667658808, -32744702856, -7327417341744, 253642619275152, 103163294897460000, -1982702662432970976, -1770895268099070677568, 4807849834551556801728, 35830291388333570578463616, 539816800507699929385760640
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 18/29, -1358/841, -84996/24389, 5322540/707281,...

Links

Crossrefs

Cf. A009973 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(18/29)^(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, 9/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0,20],9/29]//Numerator (* Harvey P. Dale, Feb 17 2021 *)
  • PARI
    a(n)=numerator(polhermite(n, 9/29)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(18*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, 9/29).
E.g.f.: exp(18*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
Previous Showing 11-20 of 41 results. Next

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

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