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%I #18 Jun 04 2022 03:32:37
%S 1,1,5,53,924,23494,810872,36194514,2017775680,136829739216,
%T 11055586913832,1046742607228152,114550470343202880,
%U 14323855468574034720,2026669209500208676608,321743057984308274403024,56892680614922936544276480,11133427829583046292676364800,2397458024796587973818060252160
%N a(n) = Sum_{k=0..n} (-1)^(n-k)*k^n*Stirling1(n,k).
%H Vincenzo Librandi, <a href="/A128943/b128943.txt">Table of n, a(n) for n = 0..43</a>
%F E.g.f.: Sum_{n>=0} (-log(1-n*x))^n/n!.
%F a(n) = Sum_{k=0..n} abs(Stirling1(n+1,k+1))*Stirling2(n,k)*k!. - _Emanuele Munarini_, Jul 04 2011
%p 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
%t Table[Sum[Abs[StirlingS1[n+1,k+1]]StirlingS2[n,k]k!,{k,0,n}],{n,0,100}] (* _Emanuele Munarini_, Jul 04 2011 *)
%t 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 *)
%o (Maxima) makelist(sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!,k,0,n),n,0,24); /* _Emanuele Munarini_, Jul 04 2011 */
%Y Cf. A108459.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, May 09 2007
%E More terms from _Emeric Deutsch_, May 18 2007
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