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
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (8,-28, 56,-70,56,-28,8,-1).
FORMULA
From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)
G.f.: -x^7(12x^7 - 6x^6 + 88x^5 - 131x^4 - 548x^3 - 1123x^2 - 448x - 31) / ((1 - x)^8).
a(n) = 243/560n^7 - 243/16n^6 + 3591/16n^5 - 28737/16n^4 + 82257/10n^3 - 81931/4n^2 + 151931/7n, for n>6. (End)
MAPLE
pp := n - >243/560*n^7 - 243/16*n^6 + 3591/16*n^5 - 28737/16*n^4 + 82257/10*n^3 - 81931/4*n^2 + 151931/7*n; seq(pp(n), n=0..30); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
A000565:=-(12*z**7-6*z**6-131*z**4+88*z**5-1123*z**2-548*z**3-31-448*z)/(z-1)**8; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {31, 696, 5823, 29380, 108933, 327840, 848380, 1958004}, 30] (* Jean-François Alcover, Feb 10 2016 *)
PROG
(Magma) [243/560*n^7-243/16*n^6+3591/16*n^5-28737/16*n^4+ 82257/10*n^3 - 81931/4*n^2+151931/7*n: n in [7..45]]; // Vincenzo Librandi, Feb 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
STATUS
approved