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%I M4628 N1978 #32 Apr 30 2022 16:58:36
%S 1,9,46,177,571,1632,4270,10446,24244,53942,115954,242240,494087,
%T 987503,1939634,3753007,7167461,13532608,25293964,46856332,86110792,
%U 157125052,284866900,513470464,920659517,1642844485,2918680214,5164483453,9104522495,15995633440
%N G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].
%C From rook polynomials.
%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 T. D. Noe, <a href="/A001926/b001926.txt">Table of n, a(n) for n = 0..1000</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,17,7,-24,9,9,-6,-1,1).
%p A001926:=-(1+z)**2/(z**2+z-1)**3/(z-1)**4; # conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation
%t nn = 30; CoefficientList[Series[(1 + x)^2/((1 - x)^4 (1 - x - x^2)^3), {x, 0, nn}], x] (* _T. D. Noe_, Aug 17 2012 *)
%t LinearRecurrence[{7,-18,17,7,-24,9,9,-6,-1,1},{1,9,46,177,571,1632,4270,10446,24244,53942},30] (* _Harvey P. Dale_, Apr 30 2022 *)
%Y Second differences are in A002941.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E Edited by _N. J. A. Sloane_, Apr 10 2009
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