A001759 Number of permutations of [n] with n-3 sequences. (Formerly M2150 N0857)

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

Offset

4,1

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).

Links

Table of n, a(n) for n=4..21.

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

Example

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

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

Crossrefs

Cf. A001250, A001758.

Sequence in context: A035601 A281124 A244721 * A243475 A019441 A147537

Adjacent sequences: A001756 A001757 A001758 * A001760 A001761 A001762

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved