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A000476 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 places.
(Formerly M4970 N2133)
7
15, 72, 609, 4960, 46188, 471660, 5275941, 64146768, 842803767, 11902900380, 179857257960, 2895705788736, 49491631601635, 895010868095256, 17074867330880805, 342733960299356800, 7220616209235766260, 159312370008282356844, 3673720238903201471593 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
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
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
FORMULA
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
MAPLE
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
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, 1], {n, 5, 23}] (* Jean-François Alcover, Sep 01 2011, after Maple prog. *)
CROSSREFS
Sequence in context: A212097 A212098 A053531 * A002603 A212562 A212092
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
STATUS
approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)