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A140325
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a(n) = binomial(n+8,8) * 2^n.
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13
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1, 18, 180, 1320, 7920, 41184, 192192, 823680, 3294720, 12446720, 44808192, 154791936, 515973120, 1666990080, 5239111680, 16066609152, 48199827456, 141764198400, 409541017600, 1163958681600, 3259084308480, 9001280471040
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OFFSET
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0,2
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COMMENTS
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With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly eight (8) u's. See example.
Number of 8D hypercubes in an (n+8)-dimensional hypercube. [Zerinvary Lajos, Jan 29 2010]
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LINKS
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FORMULA
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a(n) = Sum_{i=8..n+8} binomial(i,8)*binomial(n+8,i). Example: for n=6, a(6) = 1*3003 + 9*2002 + 45*1001 + 165*364 + 495*91 + 1287*14 + 3003*1 = 192192. - Bruno Berselli, Mar 23 2018
Sum_{n>=0} 1/a(n) = 1276/105 - 16*log(2).
Sum_{n>=0} (-1)^n/a(n) = 34992*log(3/2) - 496548/35. (End)
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EXAMPLE
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Example: a(1)=18 because we have uuuuuuuuv, uuuuuuuvu, uuuuuuvuu, uuuuuvuuu, uuuuvuuuu, uuuvuuuuu, uuvuuuuuu, uvuuuuuuu, vuuuuuuuu, uuuuuuuuz, uuuuuuuzu, uuuuuuzuu, uuuuuzuuu, uuuuzuuuu, uuuzuuuuu, uuzuuuuuu, uzuuuuuuu and zuuuuuuu.
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MAPLE
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seq(binomial(n+8, 8)*2^n, n=0..28);
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MATHEMATICA
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Table[Binomial[n + 8, 8] 2^n, {n, 0, 20}] (* Zerinvary Lajos, Jan 29 2010 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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