OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..43
FORMULA
E.g.f.: Sum_{n>=0} (-log(1-n*x))^n/n!.
a(n) = Sum_{k=0..n} abs(Stirling1(n+1,k+1))*Stirling2(n,k)*k!. - Emanuele Munarini, Jul 04 2011
MAPLE
with(combinat): a:=n->sum((-1)^(n-k)*k^n*stirling1(n, k), k=0..n): seq(a(n), n=0..18); # Emeric Deutsch, May 18 2007
MATHEMATICA
Table[Sum[Abs[StirlingS1[n+1, k+1]]StirlingS2[n, k]k!, {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Jul 04 2011 *)
nmax = 20; CoefficientList[Series[1 + Sum[(-Log[1 - k*x])^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 04 2022 *)
PROG
(Maxima) makelist(sum(abs(stirling1(n+1, k+1))*stirling2(n, k)*k!, k, 0, n), n, 0, 24); /* Emanuele Munarini, Jul 04 2011 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, May 09 2007
EXTENSIONS
More terms from Emeric Deutsch, May 18 2007
STATUS
approved