|
%I M4610 N1967 #30 Jun 28 2015 10:30:29
%S 9,30,180,980,8326,70272,695690,7518720,89193276,1148241458,
%T 15947668065,237613988040,3780133322620,63945806121448,
%U 1146081593303784,21693271558730304,432411684714253605,9053476937543082240,198641103956454088919
%N Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places.
%D J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%F 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
%p 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
%t 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-François Alcover_, May 27 2011, after Maple prog. *)
%Y Cf. A000500, A000470, A000492, A000476, A000380, A000388.
%K nonn
%O 4,1
%A _N. J. A. Sloane_
%E More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
