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A000380 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-3 places.
(Formerly M4071 N1686)
7
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; text; internal format)
OFFSET

3,1

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=3..23.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

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). - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

MAPLE

seq(f(n, 3), n=3..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, 3], {n, 3, 23}] (* Jean-Fran├žois Alcover, Sep 01 2011, after Maple prog. *)

CROSSREFS

Cf. A000500, A000470, A000440, A000476, A000492, A000388.

Sequence in context: A038262 A054102 A261063 * A154153 A164640 A223852

Adjacent sequences:  A000377 A000378 A000379 * A000381 A000382 A000383

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 March 23 19:17 EDT 2017. Contains 283957 sequences.