A000470 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places.

13, 72, 595, 4096, 39078, 379760, 4181826, 49916448, 647070333, 9035216428, 135236990388, 2159812592384, 36658601139066, 658942295734944, 12504663617290908, 249823152134646144, 5241223014084306270, 115206851288747267148, 2647678812396326064043

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn

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

• J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

Crossrefs

Cf. A000500, A000492, A000440, A000476, A000380, A000388.

Programs

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. *)

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

Extensions

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001