A001759 Number of permutations of [n] with n-3 sequences.

2, 28, 236, 1852, 14622, 119964, 1034992, 9434444, 90968602, 927367340, 9982234068, 113261721276, 1352111669942, 16950982295356, 222752212005464, 3062768908594348, 43987314357078642, 658804420084315212

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			2*x^4 + 28*x^5 + 236*x^6 + 1852*x^7 + 14622*x^8 + 119964*x^9 + 1034992*x^10 + ... . - _Michael Somos_, Aug 28 2012
		

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
• 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).

Crossrefs

Cf. A001250, A001758.

Programs

Maple

seq(coeff(series(2*tan(t)*sec(t)^2+4*sec(t)+5*tan(t)-4*sec(t)*tan(t)-1-4*sec (t)^2-t*sec(t)*tan(t)+2*sec(t)^3-t*sec(t)^2,t,30),t,i)*i!,i=4..24); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001

Formula

From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001: (Start)

E.g.f.: (1/2)*u(x)^3+(11/2)*u(x)-2*u(x)^2-(x/2)*u(x)^2+x/2, where u(x)=sec(x)+tan(x), n>3.

a(n) ~ 2n!(2/Pi)^(n+1)((4n^2+12n+8)/(Pi^2)-8(n+1)/Pi+5-n). (End)

E.g.f.: (5 * cos(x) + 2*x * sin(x) - 3*x - 4) / (1 - sin(x)) + (1 + sin(x)) / ((1 - sin(x)) * cos(x)) - 2. - Michael Somos, Aug 28 2012

a(n) = (1/2)*A001758(n) - A001758(n-1) - ((n-1)/2)*A001250(n) if n>2. - Michael Somos, Aug 28 2012

Extensions

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001

Offset corrected by N. J. A. Sloane, Aug 27 2012 at the suggestion of Michael Somos