A001344 a(n) = Sum_{k=0..2} (n+k)! * C(2,k). (Formerly M1405 N0548)

2, 5, 11, 38, 174, 984, 6600, 51120, 448560, 4394880, 47537280, 562464000, 7224940800, 100111334400, 1488257971200, 23625316915200, 398840682240000, 7134671351808000, 134805535248384000, 2682594582700032000, 56078391288471552000, 1228615514129203200000

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: A195985 A367969 A056301 * A056302 A276547 A065850

Adjacent sequences: A001341 A001342 A001343 * A001345 A001346 A001347

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved