login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..19.

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

Adjacent sequences:  A205803 A205804 A205805 * A205807 A205808 A205809

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 02 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 11:01 EDT 2021. Contains 346273 sequences. (Running on oeis4.)