0,2

For n >= 1 a(n) is the size of the centralizer of a transposition in the symmetric group S_(n+1). - Ahmed Fares (ahmedfares(AT)my-deja.com), May 12 2001

For n>0, a(n)=n!-A062119(n-1) = number of permutations of length n that have two specified elements adjacent. For example, a(4)=12 as of the 24 permutations, 12 have say 1 and 2 adjacent: 1234, 2134, 1243, 2143, 3124, 3214, 4123, 4213, 3412, 3421, 4312, 4321. - Jon Perry (perry(AT)globalnet.co.uk), Jun 08 2003

With different offset, denominators of certain sums computed by Ramanujan.

Stirling transform of a(n)=[2,4,12,48,240,...] is A000629(n)=[2,6,26,150,1082,..]. - Michael Somos Mar 04 2004

Stirling transform of a(n-1)=[1,2,4,12,48,...] is A007047(n-1)=[1,3,11,51,299,...]. - Michael Somos Mar 04 2004

Stirling transform of a(n)=[1,4,12,48,240,...] is A002050(n)=[1,5,25,149,1081,..]. - Michael Somos Mar 04 2004

Stirling transform of 2*A006252(n)=[2,2,4,8,28,...] is a(n)=[2,4,12,48,240,...]. - Michael Somos Mar 04 2004

Stirling transform of a(n+1)=[4,12,48,240,...] is 2*A005649(n)=[4,16,88,616,...]. - Michael Somos Mar 04 2004

Stirling transform of a(n+1)=[4,12,48,240,...] is 4*A083410(n)=[4,16,88,616,...]. - Michael Somos Mar 04 2004

Number of {12,12*,21,21*}-avoiding signed permutations in the hyperoctahedral group.

Permanent of the (0,1)-matrices with (i,j)-th entry equal to 0 iff it is in the border but not the corners. The border of a matrix is defined the be the first and the last row, together with the first and the last column. The corners of a matrix is the set ot the entries (i=1,j=1),(i=1,j=n),(i=n,j=1) and (i=n,j=n). - Simone Severini (ss54(AT)york.ac.uk), Oct 17 2004

B. C. Berndt, Ramanujan's Notebooks Part V, Springer-Verlag, see p. 520.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 817

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 490

T. Mansour and J. West, Avoiding 2-letter signed patterns.

Recurrence: {a(0)=0, a(1)=2, (-1-n)*a(n+1)+a(n+2)}

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

a(n) = A090802(n, n-1) for n > 0. - Ross La Haye (rlahaye(AT)new.rr.com), Sep 26 2005

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

(PARI) a(n)=if(n<1, 0, n!*2)

a(n) = T(n,2) for n>1, where T is defined as in A080046.

Cf. A062119.

Sequence in context: A004527 A002871 A013172 this_sequence A098558 A030813 A126772

Adjacent sequences: A052846 A052847 A052848 this_sequence A052850 A052851 A052852

easy,nonn

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

More terms from Ross La Haye (rlahaye(AT)new.rr.com), Sep 26 2005