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%I #20 Dec 15 2017 06:26:39
%S 0,1,0,2,12,74,538,4682,47280,545832,7087186,102247562,1622632020,
%T 28091567594,526858343698,10641342970366,230283190930560,
%U 5315654681981354,130370767028589528,3385534663256845322
%N Moebius transform of numbers of preferential arrangements.
%C Moebius transform of A000670(n-1)=[1,1,3,13,75,...] is a(n)=[1,0,2,12,74,...]. - _Michael Somos_, Mar 04 2004
%H G. C. Greubel, <a href="/A006936/b006936.txt">Table of n, a(n) for n = 0..420</a>
%H David Feldman, <a href="/A002995/a002995_2.pdf">Counting plane trees</a>, Unpublished manuscript, 1992. (Annotated scanned copy)
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%t a[n_] := DivisorSum[n, MoebiusMu[n/#]*(#-1)!*SeriesCoefficient[1/(2-Exp[x + O[x]^#]), #-1]&]; a[0]=0; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Dec 03 2015, adapted from PARI *)
%o (PARI) a(n)=if(n<1,0,sumdiv(n,d,moebius(n/d)*(d-1)!*polcoeff(1/(2-exp(x+O(x^d))),d-1)))
%Y Cf. A000670.
%K nonn
%O 0,4
%A _N. J. A. Sloane_
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