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A000380
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Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-3 places.
(Formerly M4071 N1686)
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7
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6, 8, 40, 176, 1421, 10352, 93114, 912920, 9929997, 117970704, 1521176826, 21150414880, 315400444070, 5020920314016, 84979755347122, 1523710321272384, 28851091193764023, 575253584489378040, 12047084261153160394, 264377395040950523112, 6066972656940255290199
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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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^3 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, 3), n=3..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, 3], {n, 3, 23}] (* From Jean-François Alcover, Sep 01 2011, after Maple prog. *)
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CROSSREFS
| Cf. A000500, A000470, A000440, A000476, A000492, A000388.
Sequence in context: A025627 A038262 A054102 * A154153 A164640 A192158
Adjacent sequences: A000377 A000378 A000379 * A000381 A000382 A000383
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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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