OFFSET
0,2
FORMULA
a(n) = n!*Sum_{k=0..floor((n+1)/2)} (n-2*k+1)^(n-k)/(k!*(n-2*k+1)!). - Vladeta Jovovic, Mar 15 2008
a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * (2/LambertW(2*exp(-2)))^((n+1)/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 21 2017
EXAMPLE
E.g.f: A(x) = 1 + 2*x + 5/2*x^2 + 14/3*x^3 + 245/24*x^4 + 352/15*x^5 +...
Log(A(x)-x) = x + 2*x^2 + 5/2*x^3 + 14/3*x^4 + 245/24*x^5 + 352/15*x^6 +...
MAPLE
A138293 := proc(n)
add( (n-2*k+1)^(n-k)/k!/(n-2*k+1)!, k=0..(n+1)/2) ;
%*n! ;
end proc:
seq(A138293(n), n=0..30) ; # R. J. Mathar, May 03 2023
MATHEMATICA
nmax = 20; CoefficientList[Series[x - ProductLog[-x*E^(x^2)]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 21 2017 *)
PROG
(PARI) {a(n)=local(A=1); for(i=0, n, A=x+exp(x*A+x*O(x^n))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 13 2008
STATUS
approved