A006936 Moebius transform of numbers of preferential arrangements.

0, 1, 0, 2, 12, 74, 538, 4682, 47280, 545832, 7087186, 102247562, 1622632020, 28091567594, 526858343698, 10641342970366, 230283190930560, 5315654681981354, 130370767028589528, 3385534663256845322

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Moebius transform of A000670(n-1)=[1,1,3,13,75,...] is a(n)=[1,0,2,12,74,...]. - Michael Somos, Mar 04 2004

Links

• G. C. Greubel, Table of n, a(n) for n = 0..420
• David Feldman, Counting plane trees, Unpublished manuscript, 1992. (Annotated scanned copy)
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000670.

Programs

Mathematica

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 *)

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)))