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%I #18 Sep 08 2022 08:45:06
%S 0,1,5,23,116,669,4429,33375,283072,2673321,27845293,317274407,
%T 3926774180,52469606981,752922837861,11549166072847,188596608142560,
%U 3266826328953745,59830416584102325,1155208913864163511,23453274942011893556,499481183766226468013
%N Expansion of exp(x)*log(1-x)/(x-1).
%C 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
%H Alois P. Heinz, <a href="/A073596/b073596.txt">Table of n, a(n) for n = 0..450</a>
%F Binomial transform of A000254.
%F a(n) ~ n! * exp(1) * (log(n) + gamma), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 02 2015
%p b:= proc(n) option remember; `if`(n<2, n, n*b(n-1)+(n-1)!) end:
%p a:= proc(n) add(b(k)*binomial(n, k), k=0..n) end:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Mar 07 2018
%t nn=19;Range[0,nn]!CoefficientList[Series[Exp[x]Log[1/(1-x)]/(1-x),{x,0,nn}],x] (* _Geoffrey Critzer_, Sep 24 2013 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(exp(x)*log(1-x)/(x-1)))) \\ _G. C. Greubel_, Aug 28 2018
%o (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
%Y Cf. A000254.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Aug 28 2002
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