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A000500 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places.

%I A000500 M5223 N2273 #20 Jun 28 2015 10:31:47
%S A000500 31,304,4230,43880,547338,6924960,94714620,1375878816,21273204330,
%T A000500 348919244768,6056244249682,110955673493568,2140465858763844,
%U A000500 43379533256972640,921616584567907176,20485188316420940640,475499882089797554181,11506280235885243825696
%N A000500 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places.
%D A000500 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A000500 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000500 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000500 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%F A000500 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
%p A000500 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
%t A000500 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 *)
%Y A000500 Cf. A000492, A000470, A000440, A000476, A000380, A000388.
%K A000500 nonn
%O A000500 7,1
%A A000500 _N. J. A. Sloane_
%E A000500 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001