login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258922 E.g.f. satisfies: A(x) = 1/(3 - 2*exp(x*A(x))). 2
1, 2, 18, 302, 7562, 253542, 10685794, 543309230, 32378850042, 2214215333750, 170939286647570, 14707184259036414, 1395561779648175274, 144795755972202587462, 16308198003201872476866, 1981633767850818093910094, 258406311809937562215099482, 35994776359231593721760238102 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

E.g.f. A(x) satisfies:

(1) A(x) = (1/x) * Series_Reversion( 3*x - 2*x*exp(x) ).

(2) A(x) = 1 + (1/x) * Sum_{n>=1} d^(n-1)/dx^(n-1) 2^n * (exp(x)-1)^n * x^n / n!.

(3) A(x) = exp( Sum_{n>=1} d^(n-1)/dx^(n-1) 2^n * (exp(x)-1)^n * x^(n-1) / n! ).

a(n) = A259063(n+1) / (n+1). - Vaclav Kotesovec, Jun 19 2015

a(n) ~ (c/3)^(n+1) * n^(n-1) / (sqrt(c+1) * exp(n) * (c-1)^(2*n+1)), where c = LambertW(3*exp(1)/2). - Vaclav Kotesovec, Jun 19 2015

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 18*x^2/2! + 302*x^3/3! + 7562*x^4/4! + 253542*x^5/5! +...

where A(3*x - 2*x*exp(x)) = 1/(3 - 2*exp(x)).

MATHEMATICA

CoefficientList[1/x*InverseSeries[Series[3*x - 2*x*E^x, {x, 0, 21}], x], x] * Range[0, 20]! (* Vaclav Kotesovec, Jun 19 2015 *)

PROG

(PARI) {a(n) = local(A=1); A = (1/x)*serreverse(3*x - 2*x*exp(x +x^2*O(x^n) )); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}

{a(n)=local(A=1); A = 1 + (1/x)*sum(m=1, n+1, Dx(m-1, 2^m*(exp(x+x*O(x^n))-1)^m * x^m/m!)); n!*polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}

{a(n)=local(A=1+x+x*O(x^n)); A = exp(sum(m=1, n+1, Dx(m-1, 2^m*(exp(x+x*O(x^n))-1)^m * x^(m-1)/m!)+x*O(x^n))); n!*polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A259063, A052894, A258923.

Sequence in context: A121564 A224384 A092563 * A192555 A179497 A227325

Adjacent sequences:  A258919 A258920 A258921 * A258923 A258924 A258925

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 18 2015

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 14 00:21 EST 2017. Contains 295976 sequences.