OFFSET
1,2
FORMULA
E.g.f. A(x) satisfies: A(x) = tan(x*exp(A(x))).
a(n) ~ n^(n-1) * ((1+s^2)/exp(1-s))^n * sqrt(1+s^2)/(1+s), where s = 0.74721195516156756882... is the root of the equation (1+s^2)*arctan(s) = 1. - Vaclav Kotesovec, Jan 13 2014
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 11*x^3/3! + 96*x^4/4! + 1141*x^5/5! + 17232*x^6/6! + ...
where A( arctan(x)/exp(x) ) = x.
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[ArcTan[x] / Exp[x], {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 13 2014 *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff(serreverse(atan(X)/exp(X)), n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {a(n)=local(A=x); for(i=1, n, A=tan(x*exp(A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved