A001760 Number of permutations of [n] with n-4 sequences. (Formerly M2176 N0870)

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

Offset

1,1

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=1..17.

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)

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

Crossrefs

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

Sequence in context: A187626 A059934 A006333 * A230572 A157059 A272980

Adjacent sequences: A001757 A001758 A001759 * A001761 A001762 A001763

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved