A052877 E.g.f.: exp(x)-1+log(-1/(-2+exp(x))).

0, 2, 3, 7, 27, 151, 1083, 9367, 94587, 1091671, 14174523, 204495127, 3245265147, 56183135191, 1053716696763, 21282685940887, 460566381955707, 10631309363962711, 260741534058271803, 6771069326513690647

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 848

Crossrefs

a(n) = A000629(n-1)+1, n>0. Cf. A002050.

Programs

Maple

spec := [S,{B=Set(Z,1 <= card),C=Cycle(B),S=Union(B,C)},labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

CoefficientList[Series[E^x-1+Log[-1/(-2+E^x)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

Formula

E.g.f.: exp(x)-1+log(-1/(-2+exp(x)))

a(n) ~ (n-1)! / log(2)^n. - Vaclav Kotesovec, Sep 30 2013

Extensions

New name, using e.g.f., from Vaclav Kotesovec, Sep 30 2013