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A002409
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a(n) = 2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.
(Formerly M4939 N1668)
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21
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1, 14, 112, 672, 3360, 14784, 59136, 219648, 768768, 2562560, 8200192, 25346048, 76038144, 222265344, 635043840, 1778122752, 4889837568, 13231325184, 35283533824, 92851404800, 241413652480, 620777963520, 1580162088960
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OFFSET
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0,2
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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>5, a(n-6) is equal to the number of (n+6)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan Janjic, Jul 21 2007
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REFERENCES
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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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FORMULA
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G.f.: 1/(1-2*x)^7.
a(n) = Sum_{i=6..n+6} binomial(i,6)*binomial(n+6,i). Example: for n=5, a(5) = 1*462 + 7*330 + 28*165 + 84*55 + 210*11 + 462*1 = 14784. - Bruno Berselli, Mar 23 2018
Sum_{n>=0} 1/a(n) = 47/5 - 12*log(2).
Sum_{n>=0} (-1)^n/a(n) = 2916*log(3/2) - 5907/5. (End)
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1/(1-2x)^7, {x, 0, 40}], x] (* or *) LinearRecurrence[ {14, -84, 280, -560, 672, -448, 128}, {1, 14, 112, 672, 3360, 14784, 59136}, 40] (* Harvey P. Dale, Jan 24 2022 *)
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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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EXTENSIONS
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STATUS
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approved
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