A052865 E.g.f.: log(-1/(-1+x))^2 / (-1 + log(-1/(-1+x)))^2.

0, 0, 2, 18, 166, 1720, 20168, 265776, 3900048, 63160944, 1119902112, 21588456912, 449695165104, 10068121989120, 241142216363904, 6153066311872128, 166649425520796288, 4775084999073669888, 144324648624594398976, 4589066547251186277888

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 833

Formula

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

a(n) = sum(k=1..n, (k-1)*k!*(-1)^(n-k)*Stirling1(n,k)). - Vladimir Kruchinin, Sep 26 2011

a(n) ~ n! * exp(n)*n/(exp(1)-1)^(n+2). - Vaclav Kotesovec, Sep 29 2013

Maple

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

Mathematica

CoefficientList[Series[Log[-1/(-1+x)]^2/(-1+Log[-1/(-1+x)])^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *)

Prog

(Maxima) a(n):=sum((k-1)*k!*(-1)^(n-k)*stirling1(n, k), k, 1, n); /* Vladimir Kruchinin, Sep 26 2011 */

Crossrefs

Sequence in context: A183250 A037728 A037623 * A052883 A052665 A259880

Adjacent sequences: A052862 A052863 A052864 * A052866 A052867 A052868

Keyword

easy,nonn

Author

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

Extensions

New name using e.g.f., Joerg Arndt, Sep 30 2013

Status

approved