A013277 tanh(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, -90, 315, 2520, -42525, 340200, -3586275, 56133000, -662837175, 4767562800, -32564156625, 551675124000, -4287613955625, -143803315656000, 4293290973596625, -53086088130075000

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..448

Formula

Recurrence: 4*(n-1)*(4*n^2 - 32*n + 57)*a(n) = -8*(n-2)*n*(4*n^2 - 28*n + 39)*a(n-1) - 4*(n-1)*n*(4*n-11)*(4*n^2 - 28*n + 39)*a(n-2) - 4*(n-5)*(n-2)*(n-1)*n*(20*n^2 - 104*n + 129)*a(n-3) - (n-3)*(n-2)*(n-1)*n*(68*n^3 - 756*n^2 + 2665*n - 2877)*a(n-4) - 6*(n-4)*(n-3)*(n-2)*(n-1)*n*(8*n^3 - 96*n^2 + 356*n - 383)*a(n-5) - 5*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(4*n^2 - 24*n + 29)*a(n-6). - Vaclav Kotesovec, Feb 04 2015

a(n) ~ n! * 4 * sqrt(2) * (cos(Pi*n/2)-sin(Pi*n/2)) * (7-(-1)^n) / (25 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 04 2015

Mathematica

CoefficientList[Series[-Tanh[ArcSinh[x] - Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 04 2015 *)

Crossrefs

Sequence in context: A102936 A009192 A013273 * A190187 A144549 A280992

Adjacent sequences: A013274 A013275 A013276 * A013278 A013279 A013280

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=a(1)=0 from Vaclav Kotesovec, Feb 04 2015

Status

approved