A052801 A simple grammar: labeled pairs of sequences of cycles.

1, 2, 8, 46, 342, 3108, 33324, 411360, 5741856, 89379120, 1534623936, 28804923024, 586686138384, 12885385945248, 303537419684064, 7633673997722496, 204125888803996800, 5782960189212871680

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..417

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 759.

Formula

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

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*(k+1)!. - Vladeta Jovovic, Sep 21 2003

a(n) = D^n(1/(1-x)^2) evaluated at x = 0, where D is the operator exp(x)*d/dx. Cf. A052811. - Peter Bala, Nov 25 2011

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

From Anton Zakharov, Aug 07 2016: (Start)

a(n) = A007840(n) + A215916(n).

a(n) = Sum_{k=2..n+1} k!*s(n,k) where s(n,k) is the unsigned Stirling number of the first kind, (A132393). (End)

a(0) = 1; a(n) = Sum_{k=1..n} (k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Nov 19 2023

Maple

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

Mathematica

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

Prog

(Maxima) makelist(sum((-1)^(n-k)*stirling1(n, k)*(k+1)!, k, 0, n), n, 0, 17); /* Bruno Berselli, May 25 2011 */

Crossrefs

Cf. A215916.

Cf. A007840, A354122, A354123.

Sequence in context: A321965 A229559 A128085 * A294784 A180390 A300696

Adjacent sequences: A052798 A052799 A052800 * A052802 A052803 A052804

Keyword

easy,nonn

Author

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

Status

approved