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0, 2, 8, 24, 64, 160, 384, 896, 2048, 4608, 10240, 22528, 49152, 106496, 229376, 491520, 1048576, 2228224, 4718592, 9961472, 20971520, 44040192, 92274688, 192937984, 402653184, 838860800, 1744830464, 3623878656, 7516192768, 15569256448, 32212254720
(list;
graph;
refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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Right side of the binomial sum Sum_{i = 0..n} (n-2*i)^2 * binomial(n, i) = n*2^n. - Yong Kong (ykong(AT)curagen.com), Dec 28 2000
Let W be a binary relation on the power set P(A) of a set A having n = |A| elements such that for all elements x, y of P(A), xRy if x is a proper subset of y and there are no z in P(A) such that x is a proper subset of z and z is a proper subset of y, or y is a proper subset of x and there are no z in P(A) such that y is a proper subset of z and z is a proper subset of x. Then a(n) = |W|. - Ross La Haye, Sep 26 2007
a(n) = n with the bits shifted to the left by n places (new bits on the right hand side are zeros). - Indranil Ghosh, Jan 05 2017
Satisfies Benford's law [Theodore P. Hill, Personal communication, Feb 06, 2017]. - N. J. A. Sloane, Feb 08 2017
Also the circumference of the n-cube connected cycle graph. - Eric W. Weisstein, Sep 03 2017
a(n) is also the number of derangements in S_{n+3} with a descent set of {i, i+1} such that i ranges from 1 to n-2. - Isabella Huang, Mar 17 2018
a(n-1) is also the number of multiplications required to compute the permanent of general n X n matrices using Glynn's formula (see Theorem 2.1 in Glynn). - Stefano Spezia, Oct 27 2021
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REFERENCES
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Arno Berger and Theodore P. Hill. An Introduction to Benford's Law. Princeton University Press, 2015.
A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (4.2.2.29)
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LINKS
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FORMULA
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Main diagonal of array (A085454) defined by T(i, 1) = i, T(1, j) = 2j, T(i, j) = T(i-1, j) + T(i-1, j-1). - Benoit Cloitre, Aug 05 2003
Sum_{n>=1} 1/a(n) = log(2).
Sum_{n>=1} (-1)^(n+1)/a(n) = log(3/2).
(End)
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MAPLE
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g:=1/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)*n, n=0..34); # Zerinvary Lajos, Jan 11 2009
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MATHEMATICA
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LinearRecurrence[{4, -4}, {0, 2}, 40] (* Harvey P. Dale, Mar 02 2018 *)
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PROG
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(Haskell)
a036289 n = n * 2 ^ n
a036289_list = zipWith (*) [0..] a000079_list
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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