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A000476
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Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 places.
(Formerly M4970 N2133)
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7
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15, 72, 609, 4960, 46188, 471660, 5275941, 64146768, 842803767, 11902900380, 179857257960, 2895705788736, 49491631601635, 895010868095256, 17074867330880805, 342733960299356800, 7220616209235766260, 159312370008282356844, 3673720238903201471593
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OFFSET
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5,1
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=5..23.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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. *)
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CROSSREFS
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Cf. A000500, A000470, A000440, A000492, A000380, A000388.
Sequence in context: A212097 A212098 A053531 * A002603 A212562 A212092
Adjacent sequences: A000473 A000474 A000475 * A000477 A000478 A000479
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
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STATUS
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approved
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