A013272 tan(log(x+1)-arcsinh(x))=-1/2!*x^2+3/3!*x^3-6/4!*x^4+15/5!*x^5...

0, 0, -1, 3, -6, 15, -150, 1575, -12600, 101115, -1096200, 14293125, -185862600, 2507429925, -38410772400, 647097325875, -11267340084000, 205801851630375, -4076456247864000, 86033963719328625

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) ~ n! * (1+r) * sqrt(1+r^2) * (sin(log((r+sqrt(r^2+1))/(1+r))))^2 / ((sqrt(1+r^2)-1-r) * r^(n+1)), where r = (exp(Pi/2) - exp(-Pi/4) * sqrt(2*exp(Pi/2) - 2) - 1) / (2 - exp(Pi/2)) = -0.90796357274051249412785068262... . - Vaclav Kotesovec, Feb 03 2015

Mathematica

CoefficientList[Series[-Tan[ArcSinh[x] - Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 03 2015 *)

Crossrefs

Sequence in context: A110809 A013275 A013271 * A013278 A009196 A329124

Adjacent sequences: A013269 A013270 A013271 * A013273 A013274 A013275

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=a(1)=0 from Vaclav Kotesovec, Feb 03 2015

Status

approved