OFFSET
1,2
LINKS
FORMULA
Divides by 2n and shifts left under exponential transform.
E.g.f.: -x-LambertW(-2*x*exp(-x)). - Vladeta Jovovic, Sep 17 2003
a(n) = sum(j=1..n, j^(n-1)*2^j*(-1)^(n-j)*binomial(n,j)), n>1, a(1)=1. - Vladimir Kruchinin, Jan 24 2012
a(n) ~ sqrt(1+LambertW(-exp(-1)/2)) * n^(n-1) / (exp(n)*(-LambertW(-exp(-1)/2))^n). - Vaclav Kotesovec, Oct 05 2013
MATHEMATICA
a[n_] := Sum[j^(n-1)*2^j*(-1)^(n-j)*Binomial[n, j], {j, 1, n}]; a[1] = 1; Table[a[n], {n, 1, 17}] (* Jean-François Alcover, Feb 26 2013, after Vladimir Kruchinin *)
PROG
(Maxima) a(n):=if n=1 then 1 else sum(j^(n-1)*2^j*(-1)^(n-j)*binomial(n, j), j, 1, n); /* Vladimir Kruchinin, Jan 24 2012 */
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Dec 15 1999
STATUS
approved