A007758 a(n) = 2^n*n^2.

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

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).

Index entries for sequences related to Benford's law.

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<<n \\ Charles R Greathouse IV, Oct 28 2014

Crossrefs

Cf. A014477, A248917, A355234.

Sequence in context: A359519 A209538 A006729 * A207874 A208374 A207677

Adjacent sequences: A007755 A007756 A007757 * A007759 A007760 A007761

Keyword

nonn,easy

Author

David J. Snook (ua532(AT)freenet.victoria.bc.ca)

Status

approved