0,2

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

Let M be the n X n matrix with M( i, i ) = i+1, other entries = 1. Then a(n) = det(M); example : a(3) = 17 = det([2, 1, 1; 1, 3, 1; 1, 1, 4]) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 13 2005.

With offest 1: number of permutations of the n-set into at most two cycles. [From Joerg Arndt (arndt(AT)jjj.de), Jun 22 2009]

J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups. Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

C. Lenormand, Arbres et permutations II, see p. 9

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

E.g.f.: A(x) = (1-x)^-1 * (1 - log(1-x))

a(n+1)=n*a(n) + (n-1)! - Jon Perry (perry(AT)globalnet.co.uk), Sep 26 2004

(1-x)^-1 * (1 - log(1-x)) = 1 + 2*x + 5/2*x^2 + 17/6*x^3 + ...

A000774 := proc(n) local i, j; j := 0; for i to n do j := j+1/i od; (j+1)*n! end;

ZL :=[S, {S = Set(Cycle(Z), 3 > card)}, labelled]: seq(combstruct[count](ZL, size=n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008

Cf. A000254. Same as A081046 apart from signs.

Sequence in context: A007868 A136726 A112831 this_sequence A081046 A118100 A129591

Adjacent sequences: A000771 A000772 A000773 this_sequence A000775 A000776 A000777

nonn

N. J. A. Sloane (njas(AT)research.att.com).