A013323 Numerator of [x^n] in the Taylor series arccosh(exp(x)-arcsinh(x)).

1, 1, -1, -14, 47, 3527, -4787, -6421, 11467, 523798423, -3983516101, -1424955853, 1543134469573, 2574843844561, -116899300585349, -130778050341326449, 86229762965796109, 597078237074537664671, -6594717149102687675207, -11432837331477346049407, 10146256038508134909494281

Offset

1,4

Comments

The inner function has the e.g.f. exp(x)-arcsinh(x) = 1 + 0*x/1! + 1*x^2/2! + 2*x^3/3! + 1*x^4/4! - 8*x^5/5! + 1*x^6/6! + 226*x^7/7! + 1*x^8/8! - 11024*x^9/9! + ...

Links

Table of n, a(n) for n=1..21.

Example

x + x^2/3 - x^3/18 - 14*x^4/135 + 47*x^5/3240 + 3527*x^6/68040 - 4787*x^7/680400 - ...

Crossrefs

Sequence in context: A243041 A243042 A243043 * A205475 A205753 A332606

Adjacent sequences: A013320 A013321 A013322 * A013324 A013325 A013326

Keyword

sign,frac

Author

Patrick Demichel

Extensions

Values replaced by numerators by R. J. Mathar, Dec 22 2011

More terms from Jason Yuen, Sep 29 2025

Status

approved