OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
E.g.f.: (log(1/(1-x))+x/(1-x))*(1/(1-x)^x-1)/(x*log(1/(1-x))).
a(n) ~ n! * n/log(n) * (1 + (1-gamma)/log(n) + (gamma^2 - 2*gamma + 2 - Pi^2/6)/log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 22 2016
MATHEMATICA
Table[(n+1)!*Sum[k!*StirlingS1[n-k, k+1]*(-1)^(n+1)/(n-k)!/(k+1)!, {k, 0, (n-1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 22 2016 *)
PROG
(Maxima)
makelist((n)!*coeff(taylor((log(1/(1-x))+x/(1-x))*(1/(1-x)^x-1)/(x*log(1/(1-x))), x, 0, 15), x, n), n, 0, 15);
a(n):=(n+1)!*sum((k)!*stirling1(n-k, k+1)*(-1)^(n+1)/(n-k)!/(k+1)!, k, 0, (n-1)/2);
(PARI) for(n=0, 20, print1((n+1)!*sum(k=0, (n-1)/2, k!*stirling(n-k, k+1, 1)*(-1)^(n+1)/(n-k)!/(k+1)!), ", ")) \\ G. C. Greubel, Sep 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 22 2016
STATUS
approved