A012521 - OEIS

%I #18 Oct 24 2013 10:14:46

%S 0,1,2,6,32,240,2192,23856,303872,4427520,72545792,1320608256,

%T 26445350912,577722163200,13672510932992,348466876717056,

%U 9515645659185152,277168473987809280,8577847096804769792,281084141232170336256,9722444816080638574592,353990026542011001077760

%N E.g.f.: arctanh(sinh(x)*exp(x)).

%F E.g.f.: A(x) = arctanh(x) o x/(1-x) o tanh(x), a composition of functions involving tanh(x) and its inverse; thus, the n-th iteration of A(x) equals arctanh(x) o x/(1-n*x) o tanh(x). [From Paul D. Hanna, Nov 29 2011]

%F a(n) ~ (n-1)! * 2^(n-1) / (log(3))^n. - _Vaclav Kotesovec_, Oct 24 2013

%e E.g.f.: x + 2/2!*x^2 + 6/3!*x^3 + 32/4!*x^4 + 240/5!*x^5 +...

%t With[{nn=20},CoefficientList[Series[ArcTanh[Sinh[x]Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 14 2012 *)

%o (PARI){a(n)=n!*polcoeff(subst(atanh(x+x*O(x^n)),x,subst(x/(1-x),x,tanh(x+x*O(x^n)))),n)} /* Paul D. Hanna */

%K nonn

%O 0,3

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

%E Prepended a(0)=0, _Joerg Arndt_, Oct 14 2012