A001760 Number of permutations of [n] with n-4 sequences.

2, 60, 836, 9576, 103326, 1106820, 12062152, 135391872, 1575253690, 19058801580, 240134763948, 3152151344088, 43098592576694, 613444153400340, 9082400109162224, 139747529003597424, 2232451845925297938

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

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

Programs

Maple

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

Formula

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

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.

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)

Extensions

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