A073596 Expansion of e.g.f. exp(x) * log(1-x)/(x-1).

0, 1, 5, 23, 116, 669, 4429, 33375, 283072, 2673321, 27845293, 317274407, 3926774180, 52469606981, 752922837861, 11549166072847, 188596608142560, 3266826328953745, 59830416584102325, 1155208913864163511, 23453274942011893556, 499481183766226468013

Offset: 0

Author

Vladeta Jovovic, Aug 28 2002

Keywords

• easy
• nonn

Comments

a(n) is the total number of cycles obtained by permuting the elements in every subset of {1,2,...,n}. - Geoffrey Critzer, Sep 24 2013

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Column k=2 of A269951 (with a different offset).

Cf. A000254.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x)*Log(1-x)/(x-1))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Aug 28 2018

Maple

b:= proc(n) option remember; `if`(n<2, n, n*b(n-1)+(n-1)!) end:
a:= proc(n) add(b(k)*binomial(n, k), k=0..n) end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 07 2018

Mathematica

nn=19;Range[0,nn]!CoefficientList[Series[Exp[x]Log[1/(1-x)]/(1-x),{x,0,nn}],x] (* Geoffrey Critzer, Sep 24 2013 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(exp(x)*log(1-x)/(x-1)))) \\ G. C. Greubel, Aug 28 2018

Formula

Binomial transform of A000254.

a(n) ~ n! * exp(1) * (log(n) + gamma), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 02 2015