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 A000159 Coefficients of ménage hit polynomials. (Formerly M1834 N0728) 4
 2, 8, 20, 152, 994, 7888, 70152, 695760, 7603266, 90758872, 1174753372, 16386899368, 245046377410, 3910358788256, 66323124297872, 1191406991067168, 22596344660865282, 451208920617687720, 9461897733571886372, 207894669895136763704, 4776019866458134139042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197. 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 Sean A. Irvine, Table of n, a(n) for n = 3..250 Belgacem Bouras, A New Characterization of Catalan Numbers Related to Hankel Transforms and Fibonacci Numbers, Journal of Integer Sequences, 16 (2013), #13.3.3. M. Dougherty, C. French, B. Saderholm, W. Qian, Hankel Transforms of Linear Combinations of Catalan Numbers, J. Int. Seq. 14 (2011) # 11.5.1. FORMULA Conjecture: 2*(-252307*n + 1041077)*a(n) + (504614*n^2 - 3362985*n + 5118150)*a(n-1) + (1280831*n^2 - 7397886*n + 6461565)*a(n-2) + (746598*n^2 - 2913543*n - 1336090)*a(n-3) + (-405481*n^2 + 6175011*n - 15469320)*a(n-4) + (-375862*n^2 + 4098537*n - 8846430)*a(n-5) + 2*(-187931*n + 560630)*a(n-6) = 0. - R. J. Mathar, Nov 02 2015 a(n) = round(2*n*(4*exp(-2)*((n+3/2)*BesselK(n-1,2) - (n-9/2)*BesselK(n-2,2)) + (-1)^n)/3) for n > 11 assuming the recurrence is correct. - Mark van Hoeij, Jun 09 2019 Conjecture: a(n) + 2*a(n+p) + a(n+2*p) is divisible by p for any prime p except 3. - Mark van Hoeij, Jun 10 2019 CROSSREFS A diagonal of A058087. Cf. A000179, A000425. Sequence in context: A005559 A001471 A162585 * A358681 A090612 A355760 Adjacent sequences: A000156 A000157 A000158 * A000160 A000161 A000162 KEYWORD nonn AUTHOR N. J. A. Sloane, Simon Plouffe STATUS approved

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Last modified September 22 05:50 EDT 2023. Contains 365519 sequences. (Running on oeis4.)