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

0,3

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

Cf. A108459.

Sequence in context: A357343 A231866 A196659 * A180351 A337151 A171192

Adjacent sequences: A128940 A128941 A128942 * A128944 A128945 A128946

Keyword

easy,nonn

Author

Vladeta Jovovic, May 09 2007

Extensions

More terms from Emeric Deutsch, May 18 2007

Status

approved