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URL: https://oeis.org/A205806

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A205806
E.g.f. A(x) satisfies: A( cos(x) - exp(-x) ) = x.
0
1, 2, 11, 100, 1269, 20680, 411655, 9681040, 262644825, 8074470560, 277410402675, 10533370203200, 438024379604525, 19798139730512000, 966408931916064975, 50666524133429152000, 2839464166814487200625, 169393547843598544960000, 10717798206604377757886875
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
Sequence in context: A282640 A099169 A143135 * A220433 A318007 A243950
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 02 2012
STATUS
approved