A052811 A simple grammar: sequences of pairs of cycles.

1, 0, 2, 6, 46, 340, 3308, 36288, 460752, 6551424, 103685232, 1803956880, 34247483664, 704301934752, 15598712592864, 370149922235520, 9369093828260736, 251968378971718656, 7174943434198029312

Offset

0,3

Comments

Stirling transform of (-1)^n*a(n)=[0,2,-6,46,-340,...] is A005359(n)=[0,2,0,24,0,...]. - Michael Somos, Mar 04 2004

Links

Seiichi Manyama, Table of n, a(n) for n = 0..418

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 775

Formula

a(n) = (-1)^n*Sum_{k=0..floor(n/2)} Stirling1(n, 2*k)*(2*k)!. - Vladeta Jovovic, Sep 22 2003

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

a(n) = D^n(1/(1-x^2)) evaluated at x = 0, where D is the operator exp(x)*d/dx. Cf. A006252. - Peter Bala, Nov 25 2011

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

a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n,k) * |Stirling1(k,2)| * a(n-k). - Seiichi Manyama, May 06 2022

Maple

spec := [S, {B=Cycle(Z), C=Prod(B, B), S=Sequence(C)}, 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

(PARI) a(n)=if(n<0, 0, n!*polcoeff(1/(1-log(1-x)^2), n))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, binomial(i, j)*abs(stirling(j, 2, 1))*v[i-j+1])); v; \\ Seiichi Manyama, May 06 2022
(PARI) a(n) = sum(k=0, n\2, (2*k)!*abs(stirling(n, 2*k, 1))); \\ Seiichi Manyama, May 06 2022
(Maxima) makelist((-1)^n*sum(stirling1(n, 2*k)*(2*k)!, k, 0, floor(n/2)), n, 0, 18);  \\ Bruno Berselli, May 25 2011

Crossrefs

Cf. A346921.

Sequence in context: A136557 A092662 A371341 * A078603 A316073 A001587

Adjacent sequences: A052808 A052809 A052810 * A052812 A052813 A052814

Keyword

easy,nonn

Author

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

Status

approved