|
| |
|
|
A000470
|
|
Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places.
(Formerly M4901 N2101)
|
|
6
|
|
|
|
13, 72, 595, 4096, 39078, 379760, 4181826, 49916448, 647070333, 9035216428, 135236990388, 2159812592384, 36658601139066, 658942295734944, 12504663617290908, 249823152134646144, 5241223014084306270, 115206851288747267148, 2647678812396326064043
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
5,1
|
|
|
REFERENCES
|
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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
|
|
|
|
FORMULA
|
a(n) = coefficient of y^5 in sum_0^n sigma_{n, k}(n - k)!(y - 1)^k on y where the sigma_{n, k} have generating function sigma(t, u) = (1 - 2t^2(u^2) - 2t^2(1 + t)u^3 + 3t^4(u^4))(1 - tu)^(-1)(1 - (1 + 2t)u - tu^2 + t^3(u^3))^(-1). - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
|
|
MAPLE
|
seq(f(n, 5), n=5..30); # code for f(n, k) is given in A000440 - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
|
|
MATHEMATICA
|
sigma[t_, u_] = (1 - 2 t^2 (u^2) - 2 t^2 (1 + t) u^3 + 3 t^4 (u^4)) (1 - t* u)^(-1) (1 - (1 + 2 t) u - t *u^2 + t^3 (u^3))^(-1); ds[t_, n_] := D[sigma[t, u], {u, n}] /. u -> 0; su[n_] := su[n] = Sum[ Coefficient[ds[t, n]/n!, t, j]*(n - j)!*(y - 1)^j, {j, 0, n}]; f[n_, k_] := Coefficient[su[n], y, k]; Table[f[n, 5], {n, 5, 23}] (* Jean-François Alcover, Sep 01 2011, after Maple prog. *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
|
|
STATUS
|
approved
|
| |
|
|
