OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Vaclav Kotesovec, Asymptotic solution of the equations using the Lambert W-function
FORMULA
a(n)=(n!*sum(m=floor((n+1)/2)..n, ((2*m-n)^(n-m))/((2*m-n)!*(n-m)!))). [Vladimir Kruchinin, Mar 09 2013]
From Vaclav Kotesovec, Aug 06 2014: (Start)
a(n) ~ n^n / (r^n * exp((2*r^2*n)/(1+2*r^2)) * sqrt(3+2*r^2 - 2/(1 + 2*r^2))), where r is the root of the equation r*exp(r^2)*(1+2*r^2) = n.
(a(n)/n!)^(1/n) ~ exp(1/(3*LambertW(2^(1/3)*n^(2/3)/3))) * sqrt(2/(3*LambertW(2^(1/3)*n^(2/3)/3))).
(End)
MATHEMATICA
With[{nn = 25}, CoefficientList[Series[Exp[x Exp[x^2]], {x, 0, nn}],
x] Range[0, nn]!] (* Bruno Berselli, Sep 14 2012 *)
PROG
(PARI)
x='x+O('x^66);
Vec(serlaplace(exp( x * exp(x^2) )))
/* Joerg Arndt, Sep 14 2012 */
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(k!*(n-2*k)!)); \\ Seiichi Manyama, Aug 18 2022
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Joerg Arndt, Sep 14 2012
STATUS
editing