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 A007758 a(n) = 2^n*n^2. 48
 0, 2, 16, 72, 256, 800, 2304, 6272, 16384, 41472, 102400, 247808, 589824, 1384448, 3211264, 7372800, 16777216, 37879808, 84934656, 189267968, 419430400, 924844032, 2030043136, 4437573632, 9663676416, 20971520000, 45365592064, 97844723712, 210453397504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS "The traveling salesman problem can be solved in time O(n^2 2^n) (where n is the size of the network to visit)." [Wikipedia] - Jonathan Vos Post, Apr 10 2006 Satisfies Benford's law [Theodore P. Hill, Personal communication, Feb 06, 2017]. - N. J. A. Sloane, Feb 08 2017 REFERENCES Arno Berger and Theodore P. Hill. An Introduction to Benford's Law. Princeton University Press, 2015. Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series") Wikipedia, Complexity. Index entries for linear recurrences with constant coefficients, signature (6,-12,8). FORMULA From Henry Bottomley, Jun 13 2001: (Start) a(n) = 2*A014477(n-1). G.f.: 2*x(1+2*x)/(1-2*x)^3. Binomial transform of A002939. Inverse binomial transform of A062189. (End) Sum_{n>=1} 1/a(n) = Pi^2/12 - (1/2)*(log(2))^2. - Benoit Cloitre, Apr 05 2002 a(n) = Sum_{k=1..n} k*2^k. - Zerinvary Lajos, Oct 09 2006 E.g.f.: exp(2*x)*(2*x + 4*x^2). - Geoffrey Critzer, Aug 28 2013 Sum_{n>=1} (-1)^(n+1)/a(n) = -Li_2(-1/2) (A355234). - Amiram Eldar, Jun 28 2022 MAPLE seq(seq(k^n*n^k, k=2..2), n=0..25); and seq(2^n*n^2, n=0..25); # Zerinvary Lajos, Jul 01 2007 MATHEMATICA Table[n^2 * 2^n, {n, 0, 31}] (* Alonso del Arte, Oct 22 2014 *) LinearRecurrence[{6, -12, 8}, {0, 2, 16}, 30] (* Harvey P. Dale, Jan 27 2017 *) PROG (Magma) [2^n*n^2: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011 (PARI) a(n)=n^2<

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Last modified February 4 04:05 EST 2023. Contains 360045 sequences. (Running on oeis4.)