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A001288
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a(n) = binomial(n,11).
(Formerly M4850 N2073)
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14
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1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716, 705432, 1352078, 2496144, 4457400, 7726160, 13037895, 21474180, 34597290, 54627300, 84672315, 129024480, 193536720, 286097760, 417225900, 600805296, 854992152, 1203322288, 1676056044
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OFFSET
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11,2
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COMMENTS
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Product of 11 consecutive numbers divided by 11!. - Artur Jasinski, Dec 02 2007
With a different offset, number of n-permutations (n>=11) of 2 objects: u,v, with repetition allowed, containing exactly (11) u's. Example: n=11, a(0)=1 because we have uuuuuuuuuuu n=12, a(1)=12 because we have uuuuuuuuuuuv, uuuuuuuuuuvu, uuuuuuuuuvuu, uuuuuuuuvuuu, uuuuuuuvuuuu, uuuuuuvuuuuu, uuuuuvuuuuuu, uuuuvuuuuuuu, uuuvuuuuuuuu, uuvuuuuuuuuu uvuuuuuuuuuu, vuuuuuuuuuuu. - Zerinvary Lajos, Aug 06 2008
Does not satisfy Benford's law (because n^11 does not, see Ross, 2012). - N. J. A. Sloane, Feb 09 2017
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 196.
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 7.
J. C. P. Miller, editor, Table of Binomial Coefficients. Royal Society Mathematical Tables, Vol. 3, Cambridge Univ. Press, 1954.
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).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
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FORMULA
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Sum_{n>=11} 1/a(n) = 11/10.
Sum_{n>=11} (-1)^(n+1)/a(n) = A001787(11)*log(2) - A242091(11)/10! = 11264*log(2) - 491821/63 = 0.9273021446... (End)
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MAPLE
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MATHEMATICA
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Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)/11!, {n, 1, 100}] (* Artur Jasinski, Dec 02 2007 *)
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PROG
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(PARI) for(n=11, 50, print1(binomial(n, 11), ", ")) \\ G. C. Greubel, Aug 31 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Some formulas for other offsets corrected by R. J. Mathar, Jul 07 2009
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STATUS
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approved
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