The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A196198 E.g.f. satisfies A(x) = exp(x/A(-x)). 5
1, 1, 3, 4, -19, -64, 1207, 5440, -164071, -954368, 39943691, 284754944, -15250391099, -128749666304, 8402599565375, 81978198409216, -6309988001033167, -69853770233675776, 6194681665486634899, 76717804389440684032 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n-1} binomial(n,k) * (n-k)^k * (-k+1)^(n-k-1) for n>0 with a(0)=1.
E.g.f. satisfies:
_ A(x) = exp(x*exp(x/A(x))).
_ A(x) = exp(x* exp(x*exp(-x*exp(x*exp(-x*exp(x*exp(-x*...))))))).
_ A(x) = exp(x*B(x)) where B(x) = exp(x/B(x)) is the e.g.f. of A141369.
E.g.f. satisfies: x/exp(-x/A(x)) = log(A(x)). - Vaclav Kotesovec, Feb 26 2014
|a(n)| ~ c * n! / (n^(3/2) * r^n), where r = 0.5098636055230131449434409623392631606695606770070519241... is the root of the equation r*exp(1/LambertW(-I/r))/I = LambertW(-I/r), and c = 0.385745347287849929987791864025522098993432068... if n is even, and c = 0.12921599603996711137996765405025929272341118... if n is odd. - Vaclav Kotesovec, Feb 26 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 4*x^3/3! - 19*x^4/4! - 64*x^5/5! +...
where log(A(x)) = x/A(-x) begins:
x/A(-x) = x + 2*x^2/2! - 3*x^3/3! - 32*x^4/4! + 105*x^5/5! + 2016*x^6/6! - 10115*x^7/7! - 282624*x^8/8! +...+ n*A141369(n-1)*x^n/n! +...
MATHEMATICA
Flatten[{1, 1, 3, Table[Sum[Binomial[n, k]*(n-k)^k*(-k+1)^(n-k-1), {k, 0, n-1}], {n, 3, 20}]}] (* Vaclav Kotesovec, Feb 26 2014 *)
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, binomial(n, k)*(n-k)^k*(-k+1)^(n-k-1)))}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x/subst(A, x, -x+x*O(x^n)))); n!*polcoeff(A, n)}
CROSSREFS
Cf. A141369.
Sequence in context: A330436 A025089 A041989 * A041561 A050214 A256605
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 30 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 11:53 EDT 2024. Contains 373429 sequences. (Running on oeis4.)