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A000440 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places.
(Formerly M4610 N1967)
7
9, 30, 180, 980, 8326, 70272, 695690, 7518720, 89193276, 1148241458, 15947668065, 237613988040, 3780133322620, 63945806121448, 1146081593303784, 21693271558730304, 432411684714253605, 9053476937543082240, 198641103956454088919 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

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=4..22.

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

FORMULA

a(n) = coefficient of y^4 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

Snkgf := (t, u) - >(1 - t*u)^( - 1)*(1 - (1 + 2*t)*u - t*u^2 + t^3*u^3)^( - 1); sigmankgf := (t, u) - >(1 - 2*t^2*u^2 - 2*t^2*(1 + t)*u^3 + 3*t^4*u^4)*Snkgf(t, u); f := (n, k) - >coeff(sum(coeff(subs(u=0, diff(sigmankgf(t, u), u$n))/n!, t, j)*(n - j)!*(y - 1)^j, j =0..n), y, k); seq(f(i, 4), i=4..30); # 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+2t) u - t*u^2 + t^3 (u^3))^(-1); ds[t_, n_] := D[sigma[t, u], {u, n}] /. u -> 0; f[n_, k_] := Coefficient[Sum[Coefficient[ds[t, n]/n!, t, j]*(n-j)!*(y-1)^j, {j, 0, n}], y, k]; Table[f[i, 4], {i, 4, 22}] (* Jean-Fran├žois Alcover, May 27 2011, after Maple prog. *)

CROSSREFS

Cf. A000500, A000470, A000492, A000476, A000380, A000388.

Sequence in context: A291919 A212517 A274998 * A161684 A054310 A072887

Adjacent sequences:  A000437 A000438 A000439 * A000441 A000442 A000443

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 September 26 06:24 EDT 2017. Contains 292502 sequences.