A128943 a(n) = Sum_{k=0..n} (-1)^(n-k)*k^n*Stirling1(n,k).

1, 1, 5, 53, 924, 23494, 810872, 36194514, 2017775680, 136829739216, 11055586913832, 1046742607228152, 114550470343202880, 14323855468574034720, 2026669209500208676608, 321743057984308274403024, 56892680614922936544276480, 11133427829583046292676364800, 2397458024796587973818060252160

Offset: 0

Author

Vladeta Jovovic, May 09 2007

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..43

Crossrefs

Cf. A108459.

Programs

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 *)

Maxima

makelist(sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!,k,0,n),n,0,24); /* Emanuele Munarini, Jul 04 2011 */

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

Extensions

More terms from Emeric Deutsch, May 18 2007