|
| |
|
|
A000476
|
|
Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 places.
(Formerly M4970 N2133)
|
|
7
| |
|
|
15, 72, 609, 4960, 46188, 471660, 5275941, 64146768, 842803767, 11902900380, 179857257960, 2895705788736, 49491631601635, 895010868095256, 17074867330880805, 342733960299356800, 7220616209235766260, 159312370008282356844, 3673720238903201471593
(list; graph; refs; listen; history; 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).
|
|
|
FORMULA
| a(n) = coefficient of y 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).
|
|
|
MAPLE
| seq(f(n, 1), n=5..30); # where code for f(n, k) is given in A000440
|
|
|
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, 1], {n, 5, 23}] (* From Jean-François Alcover, Sep 01 2011, after Maple prog. *)
|
|
|
CROSSREFS
| Cf. A000500, A000470, A000440, A000492, A000380, A000388.
Sequence in context: A168298 A126274 A053531 * A105451 A002603 A022817
Adjacent sequences: A000473 A000474 A000475 * A000477 A000478 A000479
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms, formula and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
|
| |
|
|
