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%I #10 Feb 04 2015 13:51:24
%S 0,0,-1,3,-6,15,-90,315,2520,-42525,340200,-3586275,56133000,
%T -662837175,4767562800,-32564156625,551675124000,-4287613955625,
%U -143803315656000,4293290973596625,-53086088130075000
%N tanh(log(x+1)-arcsinh(x))=-1/2!*x^2+3/3!*x^3-6/4!*x^4+15/5!*x^5...
%H Vaclav Kotesovec, <a href="/A013277/b013277.txt">Table of n, a(n) for n = 0..448</a>
%F 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
%F 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
%t CoefficientList[Series[-Tanh[ArcSinh[x] - Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 04 2015 *)
%K sign
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=a(1)=0 from _Vaclav Kotesovec_, Feb 04 2015
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