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Number of permutations of [n] with n-4 sequences.
(Formerly M2176 N0870)
1

%I M2176 N0870 #20 Dec 24 2014 19:55:03

%S 2,60,836,9576,103326,1106820,12062152,135391872,1575253690,

%T 19058801580,240134763948,3152151344088,43098592576694,

%U 613444153400340,9082400109162224,139747529003597424,2232451845925297938

%N Number of permutations of [n] with n-4 sequences.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

%F E.g.f.: (1/4)u(t)^4 + u(t)^3(-1-t/2) + u(t)^2(3+t) + (-7-t/2)u(t), where u(t) = sec(t) + tan(t), n>4.

%F a(n) ~ n!(2/Pi)^(n + 3)/(3*Pi)(4n^3 + (24 - 3*Pi^2 - 12*Pi)n^2 + (13*Pi^2 + 44 + 3*Pi^3 - 36*Pi)n - 24*Pi + 16*Pi^2 - 9*Pi^3 + 24). (End)

%p u := t->sec(t)+tan(t); seq(i!*coeff(series((1/4)*u(t)^4+u(t)^3*(-1-t/2)+u(t)^2* (3+t)+(-7-t/2)*u(t),t,35),t,i),i=5..24); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001

%Y Equals (1/3)*A001759(n+1)-(1/3)*(n-2)*A001758(n)-(2/3)*A001759(n).

%K nonn

%O 1,1

%A _N. J. A. Sloane_

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