|
| |
|
|
A000440
|
|
Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places.
(Formerly M4610 N1967)
|
|
7
|
|
|
|
9, 30, 180, 980, 8326, 70272, 695690, 7518720, 89193276, 1148241458, 15947668065, 237613988040, 3780133322620, 63945806121448, 1146081593303784, 21693271558730304, 432411684714253605, 9053476937543082240, 198641103956454088919
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
4,1
|
|
|
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
|
Table of n, a(n) for n=4..22.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
|
|
|
FORMULA
|
a(n) = coefficient of y^4 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
|
Snkgf := (t, u) - >(1 - t*u)^( - 1)*(1 - (1 + 2*t)*u - t*u^2 + t^3*u^3)^( - 1); sigmankgf := (t, u) - >(1 - 2*t^2*u^2 - 2*t^2*(1 + t)*u^3 + 3*t^4*u^4)*Snkgf(t, u); f := (n, k) - >coeff(sum(coeff(subs(u=0, diff(sigmankgf(t, u), u$n))/n!, t, j)*(n - j)!*(y - 1)^j, j =0..n), y, k); seq(f(i, 4), i=4..30); # 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+2t) u - t*u^2 + t^3 (u^3))^(-1); ds[t_, n_] := D[sigma[t, u], {u, n}] /. u -> 0; f[n_, k_] := Coefficient[Sum[Coefficient[ds[t, n]/n!, t, j]*(n-j)!*(y-1)^j, {j, 0, n}], y, k]; Table[f[i, 4], {i, 4, 22}] (* Jean-François Alcover, May 27 2011, after Maple prog. *)
|
|
|
CROSSREFS
|
Cf. A000500, A000470, A000492, A000476, A000380, A000388.
Sequence in context: A212517 A319839 A274998 * A300643 A161684 A294404
Adjacent sequences: A000437 A000438 A000439 * A000441 A000442 A000443
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
|
|
STATUS
|
approved
|
| |
|
|
