A001926 G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].
1, 9, 46, 177, 571, 1632, 4270, 10446, 24244, 53942, 115954, 242240, 494087, 987503, 1939634, 3753007, 7167461, 13532608, 25293964, 46856332, 86110792, 157125052, 284866900, 513470464, 920659517, 1642844485, 2918680214, 5164483453, 9104522495, 15995633440
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 (7,-18,17,7,-24,9,9,-6,-1,1).
Crossrefs
Second differences are in A002941.
Programs
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Maple
A001926:=-(1+z)**2/(z**2+z-1)**3/(z-1)**4; # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
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Mathematica
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 *) 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 *)
Extensions
Edited by N. J. A. Sloane, Apr 10 2009
Comments