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

%I A001759 M2150 N0857 #26 Dec 24 2014 19:54:55
%S A001759 2,28,236,1852,14622,119964,1034992,9434444,90968602,927367340,
%T A001759 9982234068,113261721276,1352111669942,16950982295356,222752212005464,
%U A001759 3062768908594348,43987314357078642,658804420084315212
%N A001759 Number of permutations of [n] with n-3 sequences.
%D A001759 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
%D A001759 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001759 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%F A001759 From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001: (Start)
%F A001759 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.
%F A001759 a(n) ~ 2n!(2/Pi)^(n+1)((4n^2+12n+8)/(Pi^2)-8(n+1)/Pi+5-n). (End)
%F A001759 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
%F A001759 a(n) = (1/2)*A001758(n) - A001758(n-1) - ((n-1)/2)*A001250(n) if n>2. - _Michael Somos_, Aug 28 2012
%e A001759 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
%p A001759 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
%Y A001759 Cf. A001250, A001758.
%K A001759 nonn
%O A001759 4,1
%A A001759 _N. J. A. Sloane_
%E A001759 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001
%E A001759 Offset corrected by _N. J. A. Sloane_, Aug 27 2012 at the suggestion of _Michael Somos_