This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000440 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places. (Formerly M4610 N1967) 7
 9, 30, 180, 980, 8326, 70272, 695690, 7518720, 89193276, 1148241458, 15947668065, 237613988040, 3780133322620, 63945806121448, 1146081593303784, 21693271558730304, 432411684714253605, 9053476937543082240, 198641103956454088919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 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^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 MAPLE 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 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 - (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. *) CROSSREFS Cf. A000500, A000470, A000492, A000476, A000380, A000388. Sequence in context: A212517 A319839 A274998 * A300643 A161684 A294404 Adjacent sequences:  A000437 A000438 A000439 * A000441 A000442 A000443 KEYWORD nonn AUTHOR EXTENSIONS More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)