|
| |
|
|
A000708
|
|
Number of quasi-alternating permutations of length n.
(Formerly M4188 N1745)
|
|
4
| |
|
|
1, 1, 0, 1, 6, 29, 150, 841, 5166, 34649, 252750, 1995181, 16962726, 154624469, 1505035350, 15583997521, 171082318686, 1985148989489, 24279125761950, 312193418011861, 4210755676649046, 59445878286889709, 876726137720576550
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| a(n) mod 10 for n>=2 is the periodic sequence repeat: 0, 1, 6, 9.
|
|
|
REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 113.
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
| M. E. Estanave, Sur les coefficients des développements en séries de tang x, séc x et d'autres fonctions. Caractères de périodicité que présentent les chiffres des unités de ces coefficients, Bulletin de la S.M.F., 30 (1902), pp. 220-226.
|
|
|
FORMULA
| E.g.f. 2*(1+x) + (1-2*cos(x))/(1-sin(x)).
a(n) = |A000111(n+1)-2*A000111(n)| . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 13 2007
|
|
|
MAPLE
| seq(i!*coeff(series(((tan(t)+sec(t))^2-4*(tan(t)+sec(t)))/2, t, 35), t, i), i=2..24);
|
|
|
PROG
| (PARI) x='x+O('x^99); Vec(serlaplace(2*(1+x)+(1-2*cos(x))/(1-sin(x))))
|
|
|
CROSSREFS
| Equals (1/2)*A001758. A diagonal of A008970.
Sequence in context: A186651 A108982 A059724 * A027248 A192481 A020090
Adjacent sequences: A000705 A000706 A000707 * A000709 A000710 A000711
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms, Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 3/12/01
Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
|
| |
|
|
