A114870 a(n) = A002627(n+1) - A002627(n) - n!.

0, 1, 5, 25, 141, 911, 6703, 55581, 513929, 5248891, 58724211, 714554633, 9397715341, 132870076119, 2009977939271, 32396622193141, 554297204755473, 10034223725151731, 191617109450287579, 3849745645109036001

Offset: 0

Author

Creighton Dement, Feb 20 2006

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A002627, A000522, A074909.

Programs

Mathematica

CoefficientList[Series[(E^x-1)/(1-x)^2,{x,0,20}],x]*Range[0,20]! (* Vaclav Kotesovec, Nov 20 2012 *)
Table[Sum[Binomial[n, k] (k + 1)!, {k, 0, n - 1}], {n, 0, 19}] (* Michael De Vlieger, Sep 27 2016 *)

Formula

E.g.f.: (exp(x)-1)/(1-x)^2. - Vaclav Kotesovec, Nov 20 2012

a(n) = Sum_{k=0..n-1} C(n,k)*(k+1)! = Sum_{k=0..n-1} A074909(n-1,k)*(k+1)!. - Anton Zakharov, Sep 26 2016