OFFSET
1,2
FORMULA
a(n) ~ n^(n-1) / (sqrt(cos(s)+sin(s)) * exp(n) * (cos(s)-sin(s))^(n-1/2)), where s = 0.5885327439818610774... is the root of the equation sin(s) = exp(-s). - Vaclav Kotesovec, Jan 26 2014
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1269*x^5/5! +...
The series reversion of the e.g.f. begins:
cos(x) - exp(-x) = x - 2*x^2/2! + x^3/3! + x^5/5! - 2*x^6/6! + x^7/7! + x^9/9! - 2*x^10/10! + x^11/11! + x^13/13! - 2*x^14/14! +...
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[Cos[x] - E^(-x), {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 26 2014 *)
PROG
(PARI) {a(n)=n!*polcoeff(serreverse(cos(x+x^2*O(x^n))-exp(-x+x^2*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 02 2012
STATUS
approved