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A000492 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-6 places.

%I A000492 M5092 N2204 #21 Feb 09 2016 03:01:51
%S A000492 20,154,1676,14292,155690,1731708,21264624,280260864,3970116255,
%T A000492 60113625680,969368687752,16588175089420,300272980075896,
%U A000492 5733025551810600,115148956467702600,2427199940533198992,53576182138937428377,1235917889588345408586
%N A000492 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-6 places.
%D A000492 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A000492 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000492 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000492 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%F A000492 a(n) = coefficient of y^6 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 A000492 seq(f(n,6), n=6..30); # code for f(n,k) is given in A000440 - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
%t A000492 sigma[t_, u_] = (1-2t^2 (u^2) - 2t^2 (1+t) u^3 + 3t^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]; a[n_] := f[n, 6]; Table[a[n], {n, 6, 25}] (* _Jean-François Alcover_, Feb 09 2016 *)
%Y A000492 Cf. A000500, A000470, A000440, A000476, A000380, A000388.
%K A000492 nonn
%O A000492 6,1
%A A000492 _N. J. A. Sloane_
%E A000492 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001