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%I M4970 N2133 #25 Jun 28 2015 10:29:17
%S 15,72,609,4960,46188,471660,5275941,64146768,842803767,11902900380,
%T 179857257960,2895705788736,49491631601635,895010868095256,
%U 17074867330880805,342733960299356800,7220616209235766260,159312370008282356844,3673720238903201471593
%N Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 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 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,1), n=5..30); # where 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, 1], {n, 5, 23}] (* _Jean-François Alcover_, Sep 01 2011, after Maple prog. *)
%Y Cf. A000500, A000470, A000440, A000492, A000380, A000388.
%K nonn
%O 5,1
%A _N. J. A. Sloane_
%E More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
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