|
| |
|
|
A000590
|
|
13C(2n,n-6)/(n+7).
(Formerly M4908 N2104)
|
|
4
| |
|
|
1, 13, 104, 663, 3705, 19019, 92092, 427570, 1924065, 8454225, 36463440, 154969620, 650872404, 2707475148, 11173706960, 45812198536, 186803188858
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 6,2
|
|
|
COMMENTS
| Number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) which touch but do not cross the line x-y=6. - Herbert Kociemba (kociemba(AT)t-online.de), May 24 2004
Number of standard tableaux of shape (n+6,n-6). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
|
|
|
REFERENCES
| A. Papoulis, A new method of inversion of the Laplace transform, Quart. Applied Math. 14 (1956), 405ff.
J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222.
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
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
|
|
|
FORMULA
| G.f.=x^6*C(x)^13, where C(x)=[1-sqrt(1-4x)]/(2x) is g.f. for the Catalan numbers (A000108). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
Let A be the Toeplitz matrix of order n defined by: A[i,i-1]=-1, A[i,j]=Catalan(j-i), (i<=j), and A[i,j]=0, otherwise. Then, for n>=12, a(n-6)=(-1)^(n-12)*coeff(charpoly(A,x),x^12). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
|
|
|
CROSSREFS
| Sequence in context: A129762 A023011 A022641 * A052065 A041316 A080422
Adjacent sequences: A000587 A000588 A000589 * A000591 A000592 A000593
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
