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!)
A206404 E.g.f. A(x) satisfies: exp(-A(x)) = exp(-A(x)^2) - x, with A(0) = 0. 4
1, 3, 26, 364, 7074, 176108, 5348132, 191725840, 7924856460, 371061933552, 19411323110904, 1122067341369984, 71024428188382200, 4885895673623299008, 362955565203398550768, 28957167717593649778176, 2469386593299982674585744, 224154175905500071395278592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

E.g.f.: A(x) = Series_Reversion( exp(-x^2) - exp(-x) ).

a(n) ~ sqrt((1-2*s)/(2+2*s-4*s^2)) * n^(n-1) / (exp(1-s^2)-exp(1-s))^n, where s = 0.393815762008795197237... is the root of the equation exp(s^2) = 2*s*exp(s). - Vaclav Kotesovec, Jan 12 2014

EXAMPLE

E.g.f.: A(x) = x + 3*x^2/2! + 26*x^3/3! + 364*x^4/4! + 7074*x^5/5! +...

where A( exp(-x^2) - exp(-x) ) = x.

Related expansions:

exp(-A(x)) = 1 - x - 2*x^2/2! - 18*x^3/3! - 250*x^4/4! - 4840*x^5/5! +...

exp(-A(x)^2) = 1 - 2*x^2/2! - 18*x^3/3! - 250*x^4/4! - 4840*x^5/5! +...

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[Exp[-x^2] - Exp[-x], {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 12 2014 *)

PROG

(PARI) {a(n)=local(X=x+x*O(x^n)); if(n<1, 0, n!*polcoeff(serreverse(exp(-X^2) - exp(-X)), n))}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A138014, A206401, A206402, A206403, A206405.

Sequence in context: A339298 A328269 A136046 * A262301 A317654 A143155

Adjacent sequences:  A206401 A206402 A206403 * A206405 A206406 A206407

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 07 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 November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)