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Search: id:A000440
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| A000440 |
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Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places.
(Formerly M4610 N1967)
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+0
8
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| 9, 30, 180, 980, 8326, 70272, 695690, 7518720, 89193276, 1148241458, 15947668065, 237613988040, 3780133322620, 63945806121448, 1146081593303784, 21693271558730304, 432411684714253605, 9053476937543082240, 198641103956454088919
(list; graph; listen)
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OFFSET
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4,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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FORMULA
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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).
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MAPLE
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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);
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CROSSREFS
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Cf. A000500, A000470, A000492, A000476, A000380, A000388.
Sequence in context: A084370 A000439 A002414 this_sequence A161684 A054310 A072887
Adjacent sequences: A000437 A000438 A000439 this_sequence A000441 A000442 A000443
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, formula and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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