|
| |
|
|
A001344
|
|
a(n) = sum_{k=0..2} (n+k)! * C(2,k).
(Formerly M1405 N0548)
|
|
5
|
|
|
|
2, 5, 11, 38, 174, 984, 6600, 51120, 448560, 4394880, 47537280, 562464000, 7224940800, 100111334400, 1488257971200, 23625316915200, 398840682240000, 7134671351808000, 134805535248384000, 2682594582700032000, 56078391288471552000, 1228615514129203200000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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.
Index entries for sequences related to factorial base representation
|
|
|
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
|
Cf. A000142, A007623, A028387, A336600.
From a(1) = 11 onward row 2 of A276588, row 8 of A276955.
Sequence in context: A131581 A195985 A056301 * A056302 A276547 A065850
Adjacent sequences: A001341 A001342 A001343 * A001345 A001346 A001347
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
