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.

Showing 1-10 of 10 results.

A009439 Expansion of e.g.f. log(1+x)/exp(tanh(x)).

Original entry on oeis.org

0, 1, -3, 8, -16, 29, -191, 1980, -14456, 85713, -657171, 7877880, -97759608, 1100545341, -13021637695, 185198054748, -2933940050000, 46990261427073, -774002505048195, 13811029423532424, -266175983849182016
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009438.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Tanh(x)) ))); // G. C. Greubel, Sep 08 2023
  • Mathematica
    With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Tanh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2023 *)
  • SageMath
    def A009439_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-tanh(x)) ).egf_to_ogf().list()
A009439_list(31) # G. C. Greubel, Sep 08 2023

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified and previous Mathematica program replaced by Harvey P. Dale, May 19 2023

A009435 Expansion of e.g.f.: log(1+x)/cosh(x).

Original entry on oeis.org

0, 1, -1, -1, 0, 29, -105, 139, -2072, 31737, -247545, 1824151, -22456104, 313750293, -3929185169, 51584719523, -793292190480, 13137192234225, -221862616530705, 3947317975733039, -75492532592047280, 1522475446731094285
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009434, A009436 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(x) ))); // G. C. Greubel, Sep 06 2023
  • Mathematica
    With[{nn=30},CoefficientList[Series[Log[1+x]/Cosh[x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Oct 01 2014 *)
  • PARI
    my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(x)))) \\ Joerg Arndt, Sep 06 2023
  • SageMath
    def A009435_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(x) ).egf_to_ogf().list()
A009435_list(40) # G. C. Greubel, Sep 06 2023

Formula

a(n) ~ (-1)^(n+1) * (n-1)! / cosh(1). - Vaclav Kotesovec, Oct 01 2014

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Oct 01 2014

A009433 Expansion of e.g.f. log(1+x)/cosh(tan(x)).

Original entry on oeis.org

0, 1, -1, -1, 0, -11, 15, 27, -504, 11817, -94185, 1226455, -12442056, 155936221, -1995562569, 27870901107, -423463160400, 6793396567633, -117302680146033, 2130615128588591, -40960288523646320, 827190717641773765
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009432, A009434 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tan(x)) ))); // G. C. Greubel, Sep 06 2023
  • Mathematica
    With[{m=25}, CoefficientList[Series[Log[1+x]/Cosh[Tan[x]], {x,0,m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 06 2023 *)
CoefficientList[Series[Log[1 + x]*Sech[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
  • PARI
    my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(tan(x))))) \\ Joerg Arndt, Sep 06 2023
  • SageMath
    def A009433_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(tan(x)) ).egf_to_ogf().list()
A009433_list(40) # G. C. Greubel, Sep 06 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / cosh(tan(1)). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

A009434 Expansion of e.g.f: log(1+x)/cosh(tanh(x)).

Original entry on oeis.org

0, 1, -1, -1, 0, 69, -225, -1653, 3976, 187401, -965385, -14516745, 61266744, 3032650893, -21187300953, -491788726653, 2947006495920, 166337505847057, -1463633608132017, -46261934493321105, 358635306874354320
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009433, A009435 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tanh(x)) ))); // G. C. Greubel, Sep 06 2023
  • Mathematica
    With[{nn=20},CoefficientList[Series[Log[1+x]/Cosh[Tanh[x]],{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, Jun 19 2013 *)
  • PARI
    my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(tanh(x))))) \\ Joerg Arndt, Sep 06 2023
  • SageMath
    def A009434_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(tanh(x)) ).egf_to_ogf().list()
A009434_list(40) # G. C. Greubel, Sep 06 2023

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Jun 19 2013

A009436 Expansion of e.g.f. log(1+x)/exp(sin(x)).

Original entry on oeis.org

0, 1, -3, 8, -20, 59, -261, 1665, -12368, 99945, -888961, 8802045, -96423788, 1154791637, -14982150197, 209295667833, -3133083877248, 50039962416625, -849332973526881, 15266142375582901, -289679348425382572
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009435, A009437 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Sin(x)) ))); // G. C. Greubel, Sep 08 2023
  • Mathematica
    With[{m=30}, CoefficientList[Series[Log[1+x]/E^Sin[x], {x,0,m}], x]*Range[0,m]!] (* Vaclav Kotesovec, Jan 23 2015 *)
  • SageMath
    def A009436_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-sin(x)) ).egf_to_ogf().list()
A009436_list(31) # G. C. Greubel, Sep 08 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * exp(sin(1)). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

A009437 Expansion of e.g.f. log(1+x)/exp(sinh(x)).

Original entry on oeis.org

0, 1, -3, 8, -28, 119, -581, 3345, -22352, 170889, -1480881, 14361885, -154177068, 1814792589, -23230500541, 321160966833, -4767464107904, 75612375796689, -1275789176648193, 22815192314465685, -431023517858496044
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009436, A009438, A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Sinh(x)) ))); // G. C. Greubel, Sep 08 2023
  • Mathematica
    With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Sinh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 01 2013 *)
  • SageMath
    def A009437_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-sinh(x)) ).egf_to_ogf().list()
A009437_list(31) # G. C. Greubel, Sep 08 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * exp(sinh(1)). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified by Harvey P. Dale, Oct 01 2013

A009438 Expansion of e.g.f. log(1+x)/exp(tan(x)).

Original entry on oeis.org

0, 1, -3, 8, -32, 149, -831, 5340, -38744, 316161, -2846611, 28263960, -305651048, 3593550245, -45584631743, 622159233948, -9091059243792, 141783419182561, -2351573180823939, 41355560621409352, -768924714448510480
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009437, A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Tan(x)) ))); // G. C. Greubel, Sep 08 2023
  • Mathematica
    With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Tan[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 28 2014 *)
  • SageMath
    def A009438_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-tan(x)) ).egf_to_ogf().list()
A009438_list(31) # G. C. Greubel, Sep 08 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * exp(tan(1)). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Prior Mathematica program corrected by Harvey P. Dale, Jan 28 2014

A009432 Expansion of e.g.f. log(1+x)/cosh(sinh(x)).

Original entry on oeis.org

0, 1, -1, -1, 0, 9, -45, 447, -2744, 17553, -171585, 1757535, -19723176, 245370969, -3189613245, 44636677407, -674857335120, 10851333193249, -185485926579489, 3356664148618047, -64009236131219760, 1284480775318317225
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009431, A009433 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Sinh(x)) ))); // G. C. Greubel, Sep 08 2023
  • Mathematica
    With[{m=30}, CoefficientList[Series[Log[1+x]/Cosh[Sinh[x]], {x,0,m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 08 2023 *)
  • SageMath
    def A009432_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(sinh(x)) ).egf_to_ogf().list()
A009432_list(31) # G. C. Greubel, Sep 08 2023

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

A009427 Expansion of e.g.f. log(1+x)/cos(tan(x)).

Original entry on oeis.org

0, 1, -1, 5, -12, 109, -405, 4913, -24976, 372633, -2419425, 42646845, -338219244, 6863821509, -64452230661, 1478191260393, -16062969072000, 410493211996977, -5072547848554017, 142840036992492789, -1979718755185227180
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A009405 - A009420, A009422 - A009426, A009428 - A009439.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cos(Tan(x)) ))); // G. C. Greubel, Sep 06 2023
  • Mathematica
    With[{m=25}, CoefficientList[Series[Log[1+x]/Cos[Tan[x]], {x,0,m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 06 2023 *)
CoefficientList[Series[Log[1 + x]*Sec[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)
  • PARI
    my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cos(tan(x))))) \\ Joerg Arndt, Sep 06 2023
  • SageMath
    def A009427_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cos(tan(x)) ).egf_to_ogf().list()
A009427_list(40) # G. C. Greubel, Sep 06 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / cos(tan(1)) * (1 + tan(tan(1)) / ((cos(1))^2*n)). - Vaclav Kotesovec, Jan 27 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

A024338 Expansion of log(1+x)*log(1+tan(x))/2.

Original entry on oeis.org

0, 0, 1, -3, 15, -80, 542, -4158, 37228, -374592, 4237120, -53017712, 729890528, -10957004864, 178355968576, -3129133077376, 58889303575296, -1183497066823680, 25300855990394880, -573326855846475776
Offset: 0

Views

Author

R. H. Hardin

Keywords

Crossrefs

Cf. A009422.

Programs

  • Mathematica
    With[{nn=20},CoefficientList[Series[Log[1+x]Log[1+Tan[x]]/2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 27 2011 *)

Extensions

Extended with signs, Mar 1997
Showing 1-10 of 10 results.

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