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A000388 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-2 places.
(Formerly M4139 N1717)
8

%I M4139 N1717

%S 6,20,180,1106,9292,82980,831545,9139482,109595496,1423490744,

%T 19911182207,298408841160,4770598226296,81037124739588,

%U 1457607971046492,27675791180024802,553166885187641670,11609691036091870428,255273744004170486155,5868308906885934514178

%N Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-2 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^2 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,2), n=5..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, 2], {n, 4, 23}] (* _Jean-Fran├žois Alcover_, Sep 01 2011, after Maple prog. *)

%Y Cf. A000500, A000470, A000440, A000476, A000380, A000492.

%K nonn

%O 4,1

%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 February 21 03:06 EST 2019. Contains 320364 sequences. (Running on oeis4.)