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A073596 Expansion of exp(x)*log(1-x)/(x-1). 7
0, 1, 5, 23, 116, 669, 4429, 33375, 283072, 2673321, 27845293, 317274407, 3926774180, 52469606981, 752922837861, 11549166072847, 188596608142560, 3266826328953745, 59830416584102325, 1155208913864163511, 23453274942011893556, 499481183766226468013 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

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 *)

PROG

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

(Magma) m:=30; R<x>:=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

CROSSREFS

Cf. A000254.

Sequence in context: A104090 A355055 A358607 * A167248 A321798 A005393

Adjacent sequences: A073593 A073594 A073595 * A073597 A073598 A073599

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 28 2002

STATUS

approved

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Last modified November 28 05:31 EST 2022. Contains 358407 sequences. (Running on oeis4.)