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A001926 G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].
(Formerly M4628 N1978)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From rook polynomials.
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]
MAPLE
A001926:=-(1+z)**2/(z**2+z-1)**3/(z-1)**4; # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
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 *)
CROSSREFS
Second differences are in A002941.
Sequence in context: A201458 A034487 A035039 * A213749 A085385 A217152
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Apr 10 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)