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

%I A000470 M4901 N2101 #28 Jun 28 2015 10:30:56
%S A000470 13,72,595,4096,39078,379760,4181826,49916448,647070333,9035216428,
%T A000470 135236990388,2159812592384,36658601139066,658942295734944,
%U A000470 12504663617290908,249823152134646144,5241223014084306270,115206851288747267148,2647678812396326064043
%N A000470 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places.
%D A000470 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A000470 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000470 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000470 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%F A000470 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
%p A000470 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
%t A000470 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. *)
%Y A000470 Cf. A000500, A000492, A000440, A000476, A000380, A000388.
%K A000470 nonn
%O A000470 5,1
%A A000470 _N. J. A. Sloane_
%E A000470 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001