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A054851
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a(n) = 2^(n-7)*binomial(n,7). Number of 7D hypercubes in an n-dimensional hypercube.
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16
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1, 16, 144, 960, 5280, 25344, 109824, 439296, 1647360, 5857280, 19914752, 65175552, 206389248, 635043840, 1905131520, 5588385792, 16066609152, 45364543488, 126012620800, 344876646400, 931166945280, 2483111854080
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OFFSET
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7,2
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COMMENTS
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If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>6, a(n) is equal to the number of (n+7)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan Janjic, Jul 21 2007
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LINKS
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FORMULA
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a(n) = Sum_{i=7..n} binomial(i,7)*binomial(n,i). Example: for n=11, a(11) = 1*330 + 8*165 + 36*55 + 120*11 + 330*1 = 5280. - Bruno Berselli, Mar 23 2018
Sum_{n>=7} 1/a(n) = 14*log(2) - 259/30.
Sum_{n>=7} (-1)^(n+1)/a(n) = 10206*log(3/2) - 124117/30. (End)
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MAPLE
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MATHEMATICA
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Table[2^(n-7)*Binomial[n, 7], {n, 7, 30}] (* G. C. Greubel, Aug 27 2019 *)
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PROG
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(PARI) vector(23, n, 2^(n-1)*binomial(n+6, 7)) \\ G. C. Greubel, Aug 27 2019
(Magma) [2^(n-7)*Binomial(n, 7): n in [7..30]]; // G. C. Greubel, Aug 27 2019
(GAP) List([7..30], n-> 2^(n-7)*Binomial(n, 7)); # G. C. Greubel, Aug 27 2019
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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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EXTENSIONS
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STATUS
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approved
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