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A000388
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Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-2 places.
(Formerly M4139 N1717)
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7
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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; internal format)
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OFFSET
| 4,1
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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).
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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).
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MAPLE
| seq(f(n, 2), n=5..30); #code for f(n, k) is given in A000440
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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}] (* From Jean-François Alcover, Sep 01 2011, after Maple prog. *)
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CROSSREFS
| Cf. A000500, A000470, A000440, A000476, A000380, A000492.
Sequence in context: A027148 A095854 A027268 * A175671 A069257 A133885
Adjacent sequences: A000385 A000386 A000387 * A000389 A000390 A000391
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, formula and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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