OFFSET
-1,1
COMMENTS
If we discard the first two terms and set a(0) = 11 then a(n) = (n+1)!*(n^2+7*n+11). - Gary Detlefs, Aug 11 2010
For nonnegative n, a(n) equals the permanent of the (n+2) X (n+2) matrix with a 2 in the upper right corner, a 2 in the lower left corner, and 1's everywhere else. - John M. Campbell, May 25 2011
In factorial base representation (A007623) the terms of this sequence look as: 10, 21, 121, 1210, 12100, 121000, ... From a(1)=11 onward each term begins always with "121", which is then followed by n-1 zeros. - Antti Karttunen, Sep 23 2016
a(n-2), for n > 1, is the number of linear chord diagrams on 2n vertices with one marked chord such that exactly n-2 of the remaining n-1 chords contain the marked chord, see [Young]. - Donovan Young, Aug 11 2020
REFERENCES
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).
LINKS
T. D. Noe, Table of n, a(n) for n = -1..100
E. Biondi, L. Divieti, G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35.
Donovan Young, A critical quartet for queuing couples, arXiv:2007.13868 [math.CO], 2020.
FORMULA
a(-1) = 2, for n >= 0, a(n) = A028387(1+n) * n! - Antti Karttunen, Sep 23 2016
MATHEMATICA
Join[{2}, Table[Sum[(n + k)! Binomial[2, k], {k, 0, 2}], {n, 0, 20}]] (* T. D. Noe, Jun 28 2012 *)
PROG
(Scheme) (define (A001344 n) (cond ((= -1 n) 2) (else (* (A028387 (+ 1 n)) (A000142 n))))) ;; Antti Karttunen, Sep 23 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved