A052856 E.g.f.: (1-3*exp(x)+exp(2*x))/(exp(x)-2).

1, 2, 4, 14, 76, 542, 4684, 47294, 545836, 7087262, 102247564, 1622632574, 28091567596, 526858348382, 10641342970444, 230283190977854, 5315654681981356, 130370767029135902, 3385534663256845324

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Stirling transform of A005212(n-1)=[1,1,0,6,0,120,0,...] is a(n-1)=[1,2,4,14,76,...]. - Michael Somos, Mar 04 2004

Stirling transform of (-1)^n*A052612(n-1)=[0,2,-2,12,-24,...] is a(n-1)=[0,2,4,14,76,...]. - Michael Somos, Mar 04 2004

Stirling transform of A000142(n)=[2,2,6,24,120,...] is a(n)=[2,2,4,14,76,...]. - Michael Somos, Mar 04 2004

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 824

Crossrefs

A000670(n)=a(n)-1, if n>0. A032109(n)=a(n)/2, if n>0.

A000629, A000670, A002050, A052856, A076726 are all more-or-less the same sequence. - N. J. A. Sloane, Jul 04 2012

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-3Exp[x]+Exp[x]^2)/(-2+Exp[x]),{x,0,nn}],x]Range[0,nn]!] (* Harvey P. Dale, Nov 24 2012 *)

PARI

a(n)=if(n<0,0,n!*polcoeff(subst(y+1/(1-y),y,exp(x+x*O(x^n))-1),n))

Formula

E.g.f.: (1-3*exp(x)+exp(x)^2)/(-2+exp(x))

a(n) ~ n!/(2*(log(2))^(n+1)). - Vaclav Kotesovec, Oct 05 2013

Extensions

New name using e.g.f., Vaclav Kotesovec, Oct 05 2013