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!)
A161631 E.g.f. satisfies A(x) = 1 + x*exp(x*A(x)). 10
1, 1, 2, 9, 52, 425, 4206, 50827, 713000, 11500785, 208833850, 4226139731, 94226705772, 2296472176297, 60727113115046, 1732020500240955, 52998549321251536, 1731977581804704737, 60205422811336194546 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: A(x) = 1 - LambertW(-x^2*exp(x))/x.
E.g.f.: A(x) = 1 + Sum_{n>=1} x^(2*n-1) * n^(n-1) * exp(n*x) / n!.
E.g.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where B(x) = 1 + x*exp(x)/B(x) = (1+sqrt(1+4*x*exp(x)))/2.
a(n) = n*A125500(n-1) for n>0, where exp(x*A(x)) = e.g.f. of A125500.
a(n) = n!*Sum_{k=0..n} C(n-k+1,k)/(n-k+1) * k^(n-k)/(n-k)!.
If A(x)^m = Sum_{n>=0} a(n,m)*x^n/n! then
a(n,m) = n!*Sum_{k=0..n} m*C(n-k+m,k)/(n-k+m) * k^(n-k)/(n-k)!.
a(n) ~ sqrt(1+LambertW(1/(2*exp(1/2)))) * n^(n-1) / (exp(n) * 2^(n+1/2) * (LambertW(1/(2*exp(1/2))))^(n+1)). - Vaclav Kotesovec, Jul 09 2013
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 52*x^4/4! + 425*x^5/5! +...
exp(x*A(x)) = 1 + x + 3*x^2/2! + 13*x^3/3! + 85*x^4/4! + 701*x^5/5! +...
MATHEMATICA
CoefficientList[Series[1-LambertW[-x^2*E^x]/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 09 2013 *)
PROG
(PARI) {a(n, m=1)=n!*sum(k=0, n, m*binomial(n-k+m, k)/(n-k+m)*k^(n-k)/(n-k)!)}
CROSSREFS
Sequence in context: A305304 A369090 A110322 * A121678 A124347 A360743
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 18 2009
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 May 18 19:23 EDT 2024. Contains 372665 sequences. (Running on oeis4.)