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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
 6, 20, 180, 1106, 9292, 82980, 831545, 9139482, 109595496, 1423490744, 19911182207, 298408841160, 4770598226296, 81037124739588, 1457607971046492, 27675791180024802, 553166885187641670, 11609691036091870428, 255273744004170486155, 5868308906885934514178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 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 Table of n, a(n) for n=4..23. J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy] FORMULA 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 MAPLE 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 MATHEMATICA 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-François Alcover, Sep 01 2011, after Maple prog. *) CROSSREFS Cf. A000500, A000470, A000440, A000476, A000380, A000492. Sequence in context: A027148 A095854 A027268 * A347919 A227769 A309454 Adjacent sequences: A000385 A000386 A000387 * A000389 A000390 A000391 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001 STATUS approved

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Last modified June 2 22:56 EDT 2023. Contains 363102 sequences. (Running on oeis4.)