A013190 log(cosh(x)+arcsinh(x))=x-2/3!*x^3+8/4!*x^4-12/5!*x^5-48/6!*x^6...

0, 1, 0, -2, 8, -12, -48, 432, -2112, 10000, 14080, -1500512, 17517568, -18269760, -1666201600, 16350361856, -45064462336, 922523568384, -4131436888064, -990634832194048, 21402743134224384, 92553699220882432

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) ~ 2*n^(n-1) * exp(-n) * (2*Pi*cos(n*Pi/2) + 4*cos(1)*sin(n*Pi/2)) / (2+Pi^2+2*cos(2)). - Vaclav Kotesovec, Nov 01 2013

Mathematica

CoefficientList[Series[Log[Cosh[x]+ArcSinh[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 01 2013 *)

Crossrefs

Sequence in context: A135443 A280092 A083546 * A176968 A308935 A126192

Adjacent sequences: A013187 A013188 A013189 * A013191 A013192 A013193

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Nov 01 2013

Status

approved