1,1

Number of {12,12*,1*2,21,21*}-avoiding signed permutations in the hyperoctahedral group.

a(n)=the hook product of the shape (n,1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2004

Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 01 2009: (Start)

(1+(x-1)*exp(x))/x = Sum_{k>=1} x^k/a(k).

Setting x=1 yields Sum_{k>=1} 1/a(k) = 1. (End)

Archimedeans Problems Drive, Eureka, 24 (1961), 20.

Biondi, E.; Divieti, L.; Guardabassi, G.; Counting paths, circuits, chains and cycles in graphs: A unified approach. Canad. J. Math. 22 1970 22-35.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=1..100

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 97

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 641

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 101

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

Eric Weisstein's World of Mathematics, Uniform Sum Distribution

Index entries for sequences related to factorial numbers

a(n) = (n+1)(n-1)!.

E.g.f.: x/(1-x) - ln(1-x). - Ralf Stephan, Apr 11 2004

The sequence 1, 3, 8, ... has g.f. (1+x-x^2)/(1-x)^2 and a(n)=n!(n+2-0^n) =n!A065475(n) (offset 0). - Paul Barry (pbarry(AT)wit.ie), May 14 2004

Factorial expansion of 1: 1 = sum(1/(n! + (n-1)!)) for n>0 = sum(n/(n + 1)!) for n>0. 1 = 1/2 + 1/3 + 1/8 + 1/30 + 1/144 + 1/840 + 1/5760 + 1/45360 + 1/403200 + 1/3991680 + 1/43545600..... - Claude Lenormand (claude.lenormand(AT)free.fr), Aug 24 2003

a(1)=2, a(2)=3, a(n)=(n^2-n-2)*a(n-2) for n>=3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 01 2009]

Apart from initial terms, same as A059171.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 21 2009: (Start)

Equals the square root of the first right hand column of A162990.

(End)

Sequence in context: A078918 A054104 A053556 this_sequence A141520 A072042 A162074

Adjacent sequences: A001045 A001046 A001047 this_sequence A001049 A001050 A001051

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000