A000492 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-6 places.

20, 154, 1676, 14292, 155690, 1731708, 21264624, 280260864, 3970116255, 60113625680, 969368687752, 16588175089420, 300272980075896, 5733025551810600, 115148956467702600, 2427199940533198992, 53576182138937428377, 1235917889588345408586

Offset: 6

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, A000470, A000440, A000476, A000380, A000388.

Programs

Maple

seq(f(n,6), n=6..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_] = (1-2t^2 (u^2) - 2t^2 (1+t) u^3 + 3t^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]; a[n_] := f[n, 6]; Table[a[n], {n, 6, 25}] (* Jean-François Alcover, Feb 09 2016 *)

Formula

a(n) = coefficient of y^6 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