A012758 Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).

0, 1, -1, 6, -18, 123, -855, 8610, -92540, 1220765, -17627085, 291506270, -5265113502, 105134332743, -2272750891411, 53258927842666, -1338863892701400, 36033888424535961, -1032074699069841561

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ -(-1)^n * sqrt(1/r + sqrt(1 - r^2)/exp(r)) * n^(n-1) / (exp(n*(1-r)) * (exp(r) - 1)^(n - 1/2)), where r = 0.85490459670313737191040551709068078198... is the real root of the equation 1 + sqrt(1 - r^2) = r*exp(1 - exp(-r)). - Vaclav Kotesovec, Jul 25 2018

Example

x - 1/2!*x^2 + 6/3!*x^3 - 18/4!*x^4 + 123/5!*x^5 ...

Mathematica

Range[0, 20]! CoefficientList[ Series[ArcSin[Cosh[x] Log[x + 1]], {x, 0, 20}], x] (* Robert G. Wilson v, Jul 24 2018 *)

Crossrefs

Sequence in context: A009580 A125839 A117813 * A208822 A003496 A009582

Adjacent sequences: A012755 A012756 A012757 * A012759 A012760 A012761

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

a(0) inserted and title improved by Sean A. Irvine, Jul 24 2018

Status

approved