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 A000500 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places. (Formerly M5223 N2273) 6
 31, 304, 4230, 43880, 547338, 6924960, 94714620, 1375878816, 21273204330, 348919244768, 6056244249682, 110955673493568, 2140465858763844, 43379533256972640, 921616584567907176, 20485188316420940640, 475499882089797554181, 11506280235885243825696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,1 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^7 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, 7), n=7..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 + 2*t)*u - t*u^2 + t^3*u^3)); 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]; a[n_] := f[n, 7]; Table[Print[an = a[n]]; an, {n, 7, 24}] (* Jean-François Alcover, Jan 25 2013, after Maple code *) CROSSREFS Cf. A000492, A000470, A000440, A000476, A000380, A000388. Sequence in context: A001298 A027841 A221853 * A141912 A147297 A295975 Adjacent sequences:  A000497 A000498 A000499 * A000501 A000502 A000503 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 October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)