A001925 From rook polynomials. (Formerly M4151 N1724)

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

0,2

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).

Formula

Riordan gives the g.f. (1+x)/[(1-x-x^2)^2*(1-x)^3].

Maple

A001925:=-(1+z)/(z**2+z-1)**2/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation

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 *)

Crossrefs

Cf. A002940.

Sequence in context: A053739 A280481 A055797 * A002663 A099855 A347435

Adjacent sequences: A001922 A001923 A001924 * A001926 A001927 A001928

Keyword

nonn

Author

N. J. A. Sloane

Status

approved