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 38 results. Next

A013891 a(n) = 19^(5*n + 2).

Original entry on oeis.org

361, 893871739, 2213314919066161, 5480386857784802185939, 13569980418174090907801371961, 33600614943460448322716069311260139, 83198449060887472631428936505541918917761, 206007596521214410095208558252435839890349094339
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A001029.

Programs

Formula

a(n) = 2476099*a(n-1), a(0)=361. - Vincenzo Librandi, May 27 2011

A013892 a(n) = 19^(5*n + 3).

Original entry on oeis.org

6859, 16983563041, 42052983462257059, 104127350297911241532841, 257829627945307727248226067259, 638411683925748518131605316913942641, 1580770532156861979997149793605296459437459, 3914144333903073791808962606796280957916632792441
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A001029.

Programs

  • Magma
    [19^(5*n+3): n in [0..10]]; // Vincenzo Librandi, May 27 2011
  • Mathematica
    19^(5*Range[0,10]+3) (* or *) NestList[2476099#&,6859,10] (* Harvey P. Dale, Apr 20 2013 *)

Formula

a(n) = 2476099*a(n-1), a(0)=6859. - Vincenzo Librandi, May 27 2011

A013893 a(n) = 19^(5*n + 4).

Original entry on oeis.org

130321, 322687697779, 799006685782884121, 1978419655660313589123979, 4898762930960846817716295277921, 12129821994589221844500501021364910179, 30034640110980377619945846078500632729311721, 74368742344158402044370289529129338200416023056379
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A001029.

Programs

  • Magma
    [19^(5*n+4): n in [0..10]]; // Vincenzo Librandi, May 27 2011
  • Mathematica
    NestList[2476099*# &, 130321, 10] (* Paolo Xausa, Jul 14 2025 *)

Formula

a(n) = 2476099*a(n-1), a(0)=130321. - Vincenzo Librandi, May 27 2011

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

A138130 Powers of 1729, the Hardy-Ramanujan number.

Original entry on oeis.org

1, 1729, 2989441, 5168743489, 8936757492481, 15451653704499649, 26715909255079893121, 46191807102033135206209, 79865634479415290771535361, 138087682014909037743984639169, 238753602203777726259349441123201, 412804978210331688702415183702014529
Offset: 0

Views

Author

Omar E. Pol, Mar 09 2008

Keywords

Comments

About 1729: "No," said Ramanujan, "It is a very interesting number..."

References

  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1997, p. 153.

Links

Crossrefs

Cf. A001235, A011541, A133019, A133029, A138129.
Cf. A000420, A001022, A001029.

Programs

Formula

a(n) = 1729^n.
From Chai Wah Wu, Jan 19 2021: (Start)
a(n) = 1729*a(n-1) for n > 0.
G.f.: 1/(1 - 1729*x). (End)
From Elmo R. Oliveira, Jun 23 2025: (Start)
E.g.f.: exp(1729*x).
a(n) = A000420(n)*A001022(n)*A001029(n). (End)

A159648 Numerator of Hermite(n, 10/19).

Original entry on oeis.org

1, 20, -322, -35320, -8948, 101825200, 2068806280, -399730640800, -18450359755120, 1939836986158400, 158687177411937760, -10831879491824892800, -1476931152842107545920, 64308780860328720300800, 15148651417782595832021120, -347060128580550788160064000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 20/19, -322/361, -35320/6859, -8948/130321, 101825200/2476099, ...

Links

Crossrefs

Cf. A001029 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(20/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018
  • Maple
    A159648 := proc(n)
        orthopoly[H](n,10/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n,10/19],{n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 10/19], {n,0,50}] (* G. C. Greubel, Jul 10 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,10/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 20*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 10 2018: (Start)
a(n) = 19^n * Hermite(n, 10/19).
E.g.f.: exp(20*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159649 Numerator of Hermite(n, 11/19).

Original entry on oeis.org

1, 22, -238, -37004, -298580, 100298792, 3284447224, -362236528016, -24568799886448, 1551764588318560, 193786882605147424, -6940428910346759872, -1691744857677709558592, 22913489210334717241984, 16382813996790345696268160, 128812358991324283435925248
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 22/19, -238/361, -37004/6859, -298580/130321, 100298792/2476099, ...

Links

Crossrefs

Cf. A001029 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(22/19)^(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
    A159649 := proc(n)
        orthopoly[H](n,11/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n, 11/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 11/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,11/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 22*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 19^n * Hermite(n, 11/19).
E.g.f.: exp(22*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159650 Numerator of Hermite(n, 12/19).

Original entry on oeis.org

1, 24, -146, -38160, -599604, 95815584, 4464144456, -307933642944, -29952193511280, 1059772077373824, 220063883293269216, -2370021199600548096, -1804627869905557267776, -22777205204394225722880, 16391584262028099097996416, 623630012494691211958785024
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 24/19, -146/361, -38160/6859, -599604/130321, 95815584/2476099, ...

Links

Crossrefs

Cf. A001029 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(24/19)^(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
    A159650 := proc(n)
        orthopoly[H](n,12/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n, 12/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 12/19], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,12/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 24*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 19^n * Hermite(n, 12/19).
E.g.f.: exp(24*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159651 Numerator of Hermite(n, 13/19).

Original entry on oeis.org

1, 26, -46, -38740, -907604, 88283416, 5571819256, -237576457456, -34336962413680, 479480595510176, 235588077247357216, 2663440108847816896, -1801791066668467770176, -69922612836437647611520, 15093623018002859652972416, 1099211969018786093034526976
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 26/19, -46/361, -38740/6859, -907604/130321, 88283416/2476099,..

Links

Crossrefs

Cf. A001029 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(26/19)^(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
    A159651 := proc(n)
        orthopoly[H](n,13/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n, 13/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 13/19], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,13/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -26*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 19^n * Hermite(n, 13/19).
E.g.f.: exp(26*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159652 Numerator of Hermite(n, 14/19).

Original entry on oeis.org

1, 28, 62, -38696, -1217780, 77656208, 6570559624, -152431023584, -37475677000048, -168877363780160, 238788382960467424, 7905369289385843072, -1675106997369228675392, -115395115449577347286784, 12491491044719414623199360, 1516175576216471435824394752
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2009

Keywords

Examples

			Numerator of 1, 28/19, 62/361, -38696/6859, -1217780/130321, 77656208/2476099, ...

Links

Crossrefs

Cf. A001029 (denominators).

Programs

  • Magma
    [Numerator((&+[(-1)^k*Factorial(n)*(28/19)^(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
    A159652 := proc(n)
        orthopoly[H](n,14/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
  • Mathematica
    Numerator[Table[HermiteH[n, 14/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 14/19], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)
  • PARI
    a(n)=numerator(polhermite(n,14/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -28*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 19^n * Hermite(n, 14/19).
E.g.f.: exp(28*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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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