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A000380 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-3 places.
(Formerly M4071 N1686)
7

%I M4071 N1686 #24 Jun 28 2015 10:30:05

%S 6,8,40,176,1421,10352,93114,912920,9929997,117970704,1521176826,

%T 21150414880,315400444070,5020920314016,84979755347122,

%U 1523710321272384,28851091193764023,575253584489378040,12047084261153160394,264377395040950523112,6066972656940255290199

%N Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-3 places.

%D J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

%F a(n) = coefficient of y^3 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 seq(f(n,3), n=3..30); # code for f(n,k) is given in A000440 - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

%t 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, 3], {n, 3, 23}] (* _Jean-François Alcover_, Sep 01 2011, after Maple prog. *)

%Y Cf. A000500, A000470, A000440, A000476, A000492, A000388.

%K nonn

%O 3,1

%A _N. J. A. Sloane_

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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)