A001925 From rook polynomials.
1, 6, 22, 64, 162, 374, 809, 1668, 3316, 6408, 12108, 22468, 41081, 74202, 132666, 235160, 413790, 723530, 1258225, 2177640, 3753096, 6444336, 11028792, 18818664, 32024977, 54367374, 92094334, 155688208, 262711866, 442556798, 744355673, 1250157228
Offset: 0
Keywords
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
- T. D. Noe, Table of n, a(n) for n = 0..1000
- 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 (5,-8,2,6,-4,-1,1).
Crossrefs
Cf. A002940.
Programs
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Maple
A001925:=-(1+z)/(z**2+z-1)**2/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation
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Mathematica
nn = 40; CoefficientList[Series[(1 + x)/((1 - x - x^2)^2*(1 - x)^3), {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *) LinearRecurrence[{5,-8,2,6,-4,-1,1},{1,6,22,64,162,374,809},40] (* Harvey P. Dale, Oct 15 2021 *)
Formula
Riordan gives the g.f. (1+x)/[(1-x-x^2)^2*(1-x)^3].