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!)
A161566 E.g.f. satisfies: A(x) = exp(2*x*exp(x*A(x))). 5
1, 2, 8, 62, 696, 10362, 193036, 4323846, 113288720, 3401106290, 115150465044, 4341507224958, 180422159478424, 8194551731190762, 403871802897954332, 21468380724070186358, 1224364515329753354784, 74574475891799118725346 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..367

FORMULA

a(n) = Sum_{k=0..n} 2^k * C(n,k) * (n-k+1)^(k-1) * k^(n-k).

E.g.f.: A(x) = B(x)^2 where B(x) = e.g.f. of A161567.

a(n) ~ sqrt(LambertW(1/(2*r))) * n^(n-1) / (exp(n) * r^(n+1)), where r = 0.256263163133653382... is the root of the equation 1/LambertW(1/r) = -log(2*r^2) - LambertW(1/r). - Vaclav Kotesovec, Feb 28 2014

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 8*x^2/2! + 62*x^3/3! + 696*x^4/4! +...

log(A(x)) = 2*x*C(x) where C(x) = exp(x*A(x)) = e.g.f. of A161565:

C(x) = 1 + x + 5*x^2/2! + 37*x^3/3! + 417*x^4/4! + 6201*x^5/5! +...

A(x)^(1/2) = e.g.f. of A161567:

A(x)^(1/2) = 1 + x + 3*x^2/2! + 22*x^3/3! + 233*x^4/4! + 3356*x^5/5! +...

MATHEMATICA

Flatten[{1, Table[Sum[2^k * Binomial[n, k] * (n-k+1)^(k-1) * k^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 28 2014 *)

PROG

(PARI) {a(n)=sum(k=0, n, 2^k*binomial(n, k)*(n-k+1)^(k-1)*k^(n-k))}

(PARI) {A(n)=local(A=1+x); for(i=0, n, A=exp(2*x*exp(x*A+O(x^n)))); n!*polcoeff(A, n, x)}

CROSSREFS

Cf. A161565, A161567.

Sequence in context: A116976 A132574 A086903 * A192516 A159476 A230824

Adjacent sequences:  A161563 A161564 A161565 * A161567 A161568 A161569

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 14 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 8 07:34 EDT 2020. Contains 335513 sequences. (Running on oeis4.)