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 1-2 of 2 results.

A052134 Numerators of coefficients in function a(x) such that a(a(a(x))) = sinh x.

Original entry on oeis.org

1, 1, -7, 643, -13583, 29957, -24277937, 6382646731, 2027394133729, -10948179003324221, 177623182156029053, -126604967848904128751, -2640658729595838040517543, 423778395125199663867841, 134802774190189008299452419971
Offset: 0

Views

Author

N. J. A. Sloane, Jan 22 2000

Keywords

References

  • W. C. Yang, Composition equations, preprint, 1999.

Crossrefs

Cf. A052135. See also A048602, A048603, etc.
Apart from signs, same as A052132?

Programs

  • Mathematica
    n = 15; m (* = maximal degree *)= 2n - 1; a[x_] = Sum[c[k]*x^k, {k, 1, m, 2}]; coes = DeleteCases[ CoefficientList[ Series[ a@a@a@x - Sinh[x], {x, 0, m}], x] // Rest, 0]; Do[s[k] = Solve[coes[[1]] == 0] // First; coes = coes /. s[k] // Rest, {k, 1, n}]; (CoefficientList[a[x] /. Flatten@Array[s, n], x] // Numerator // Partition[#, 2] &)[[All, 2]] (* Jean-François Alcover, Jan 04 2013 *)

Extensions

More terms from Vladeta Jovovic, Jul 16 2002

A052135 Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x.

Original entry on oeis.org

1, 18, 1080, 408240, 29393280, 215550720, 648499737600, 953294614272000, 2333665215737856000, 7183021534041120768000, 232066849561328517120000, 723095875143672151080960000, 74189636789740762700906496000000
Offset: 0

Views

Author

N. J. A. Sloane, Jan 22 2000

Keywords

Comments

Also denominators of coefficients in function a(x) such that a(a(a(x))) = sinh x.

References

  • W. C. Yang, Composition equations, preprint, 1999.

Crossrefs

Cf. A052132, A052134. See also A048602, A048603, etc.

Programs

  • Mathematica
    n = 13; m = 2 n - 1 (* m = maximal degree *); a[x_] = Sum[c[k] x^k, {k, 1, m, 2}] ; coes = DeleteCases[ CoefficientList[Series[a @ a @ a @ x - Sin[x], {x, 0, m}], x] // Rest , 0]; Do[s[k] = Solve[coes[[1]] == 0] // First; coes = coes /. s[k] // Rest, {k, 1, n}]
(CoefficientList[a[x] /. Flatten @ Array[s, n], x] // Denominator // Partition[#, 2] &)[[All, 2]]
(* Jean-François Alcover, May 04 2011 *)

Extensions

More terms from Vladeta Jovovic, Jul 16 2002
Showing 1-2 of 2 results.

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

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