OFFSET
0,2
FORMULA
E.g.f.: -(((x+1)*e^x-1)*log(-x*e^x+x+1))/(x*e^x-x).
a(n) ~ (n-1)! * (1 + 1/r + r) / r^n, where r = 0.8064659942363268087699282186454... is the root of the equation exp(r) = 1 + 1/r. - Vaclav Kotesovec, Mar 22 2016
MATHEMATICA
Table[(n+1)! * Sum[k!*StirlingS2[n-k, k+1]/(n-k)!/(k+1), {k, 0, (n-1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 22 2016 *)
PROG
(Maxima)
makelist((n)!*coeff(taylor(-(((x+1)*%e^x-1)*log(-x*%e^x+x+1))/(x*%e^x-x), x, 0, 15), x, n), n, 0, 15);
a(n):=(n+1)!*sum((k)!*stirling2(n-k, k+1)/(n-k)!/(k+1), k, 0, (n-1)/2);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 22 2016
STATUS
approved