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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A159869 Numerator of Hermite(n, 5/23).

Original entry on oeis.org

1, 10, -958, -30740, 2733292, 157424600, -12884868680, -1128180047600, 84143536968080, 10390351292567200, -697311246084385760, -116903029136204833600, 6946277990568033138880, 1553663637818936898774400, -80002471104083358804411520, -23812890514414926932690528000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 10/23, -958/529, -30740/12167, 2733292/279841

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(10/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018
  • Maple
    f:= gfun:-rectoproc({a(n) = -(1058*n-1058)*a(n-2)+10*a(n-1), a(0) = 1, a(1) = 10},a(n),remember):
map(f, [$0..40]); # Robert Israel, Dec 07 2017
  • Mathematica
    Numerator[Table[HermiteH[n, 5/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 5/23], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 5/23)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

a(n) = 10*a(n-1) + 1058*(1-n)*a(n-2). - Robert Israel, Dec 07 2017
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 23^n * Hermite(n, 5/23).
E.g.f.: exp(10*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159870 Numerator of Hermite(n, 6/23).

Original entry on oeis.org

1, 12, -914, -36360, 2464716, 183452112, -10836922296, -1294597074528, 64723081629840, 11734146618363072, -475483423858979616, -129853072308589057152, 3975439219167736085184, 1696319876659859502624000, -34322352500514728084132736, -25537758243092015689876280832
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 12/23, -914/529, -36360/12167, 2464716/279841

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(12/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 6/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 6/23], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 6/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(12*x - 529*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 23^n * Hermite(n, 6/23).
E.g.f.: exp(12*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159872 Numerator of Hermite(n, 8/23).

Original entry on oeis.org

1, 16, -802, -46688, 1798540, 226360256, -5892512504, -1531215105152, 19140505922192, 13266452744761600, 30007346525073376, -139878952495176553984, -2587288738781628813632, 1734506561058255468362752, 63337674290134610196498560, -24678108393752726234245105664
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 16/23, -802/529, -46688/12167, 1798540/279841

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(16/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 8/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 8/23], {n,0,30}] (* G. C. Greubel, Jul 15 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 8/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(16*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018

Formula

From G. C. Greubel, Jul 15 2018: (Start)
a(n) = 23^n * Hermite(n, 8/23).
E.g.f.: exp(16*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159873 Numerator of Hermite(n, 9/23).

Original entry on oeis.org

1, 18, -734, -51300, 1406316, 242415288, -3075936456, -1594219104432, -5915558486640, 13386990447152928, 297293775958538784, -136283070963624280128, -5913000241950711410496, 1623815864599061055116160, 110556090890573183732052864, -22061950950410975041203610368
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 18/23, -734/529, -51300/12167, 1406316/279841,...

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(18/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018
  • Mathematica
    HermiteH[Range[0,20],9/23]//Numerator (* Harvey P. Dale, Aug 11 2016 *)
Table[23^n*HermiteH[n, 9/23], {n,0,30}] (* G. C. Greubel, Jul 15 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 9/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(18*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018

Formula

From G. C. Greubel, Jul 15 2018: (Start)
a(n) = 23^n * Hermite(n, 9/23).
E.g.f.: exp(18*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159874 Numerator of Hermite(n, 10/23).

Original entry on oeis.org

1, 20, -658, -55480, 978892, 254369200, -90954680, -1616554775200, -31657485143920, 13049369914414400, 562429971828694240, -126813734257930467200, -9081834697300952909120, 1428390476192666153388800, 153479363950530629379812480, -18087732454355158476398656000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 20/23, -658/529, -55480/12167, 978892/279841,...

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 11/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 10/23], {n,0,30}] (* G. C. Greubel, Jul 15 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 10/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(20*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018

Formula

From G. C. Greubel, Jul 15 2018: (Start)
a(n) = 23^n * Hermite(n, 10/23).
E.g.f.: exp(20*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159875 Numerator of Hermite(n, 11/23).

Original entry on oeis.org

1, 22, -574, -59180, 519916, 261887912, 3011178424, -1596218540048, -57417595289200, 12247206626603872, 816168888129047584, -111619730570629918912, -11954207592599713998656, 1154131532287523742536320, 189809064938941988673313664, -12919196827586077923635071232
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 22/23, -574/529, -59180/12167, 519916/279841,..

Links

Crossrefs

Cf. A009967 (denominators)

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],11/23]] (* Harvey P. Dale, Nov 20 2012 *)
Table[23^n*HermiteH[n,11/23], {n,0,30}] (* G. C. Greubel, Jul 15 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 11/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(22*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018

Formula

From G. C. Greubel, Jul 15 2018: (Start)
a(n) = 23^n * Hermite(n, 11/23).
E.g.f.: exp(22*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159877 Numerator of Hermite(n, 12/23).

Original entry on oeis.org

1, 24, -482, -62352, 33420, 264675744, 6175426056, -1531951397568, -82502038912368, 10986387695118720, 1049257719206417376, -91053796553402040576, -14396552453405934395712, 810501742160249881655808, 217462224255991218838362240, -6786058422733831994965134336
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 24/23, -482/529, -62352/12167, 33420/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(24/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    HermiteH[Range[0,20],12/23]//Numerator (* Harvey P. Dale, Jan 09 2017 *)
Table[23^n*HermiteH[n, 12/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 12/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(24*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 12/23).
E.g.f.: exp(24*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159882 Numerator of Hermite(n, 13/23).

Original entry on oeis.org

1, 26, -382, -64948, -476180, 262479256, 9343452856, -1423288542832, -106203113965168, 9285433263435680, 1252687316025657376, -65670013710482402624, -16286195340379143010112, 410305415218426865451392, 234668271507253831462816640, 23931248973260886967214336
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 26/23, -382/529, -64948/12167, -476180/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 13/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 13/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 13/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(26*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 13/23).
E.g.f.: exp(26*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159883 Numerator of Hermite(n, 14/23).

Original entry on oeis.org

1, 28, -274, -66920, -1004084, 255091088, 12454154824, -1270601891552, -127812323590000, 7175629349576128, 1417946567012111584, -36215654642176309888, -17516100476867891291456, -30656862015230525822720, 240058053822414522099649664, 7175714947197201167276319232
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 28/23, -274/529, -66920/12167, -1004084/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • GAP
    List(List([0..20],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(28/23)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # Muniru A Asiru, Jul 12 2018
  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..20]]; // Vincenzo Librandi, Jun 23 2018
  • Mathematica
    Numerator[Table[HermiteH[n, 14/23], {n, 0, 40}]] (* Vincenzo Librandi, Jun 23 2018 *)
Table[23^n*HermiteH[n, 14/23], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 14/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^99); Vec(serlaplace(exp(-529*x^2+28*x))) \\ Altug Alkan, Jul 30 2018

Formula

E.g.f.: exp(-529*x^2 + 28*x). - Simon Plouffe, Jun 22 2018; corrected by G. C. Greubel, Jul 11 2018
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 23^n * Hermite(n, 14/23).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -28*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021

A159884 Numerator of Hermite(n, 15/23).

Original entry on oeis.org

1, 30, -158, -68220, -1545108, 242353800, 15444235320, -1075134862800, -146634052663920, 4700919898821600, 1537277046430494240, -3617421136617700800, -17999352900456622989120, -494053808263200360316800, 232741485544984381782852480, 14300169574344055190498016000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerators of 1, 30/23, -158/529, -68220/12167, -1545108/279841, ...

Links

Crossrefs

Cf. A009967 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(30/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
  • Mathematica
    Numerator[HermiteH[Range[0,20],15/23 ]] (* Harvey P. Dale, Nov 16 2014 *)
Table[23^n*HermiteH[n, 15/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)
  • PARI
    a(n)=numerator(polhermite(n, 15/23)) \\ Charles R Greathouse IV, Jan 29 2016
  • PARI
    x='x+O('x^30); Vec(serlaplace(exp(30*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

E.g.f.: exp(-x*(529*x-30)). - Simon Plouffe, Jun 22 2018
From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 23^n * Hermite(n, 15/23).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -30*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021
Previous Showing 21-30 of 38 results. Next

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

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