A248917 -id:A248917 - cp's OEIS frontend

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

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

"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

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.

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.

Cf. A014477, A248917, A355234.

[2^n*n^2: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011

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

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 *)

a(n)=n^2<Charles R Greathouse IV, Oct 28 2014

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

A282400 Primes of the form n^2*2^n + 1.

Original entry on oeis.org

3, 17, 73, 257, 924844033, 966367641601, 9354438770689, 468230246058455728129, 12676506002282294014967032053760001, 112418056545792871256481555812420390351647277057, 462428252436731001462884654101636424188009906177, 32113073085884097323811434312613640568611799040001

Offset: 1

Abhiram R Devesh, Feb 19 2017

Abhiram R Devesh, Table of n, a(n) for n = 1..15

Subset of A248917.
Cf. A058780 Numbers n such that n^2 * 2^n + 1 is prime.
Cf. A279904 Primes of the form n^2*2^n - 1.

Select[Table[n^2 2^n+1,{n,200}],PrimeQ] (* Harvey P. Dale, Mar 26 2023 *)

import sympy
n = 1
while n < 100:
    q = (n**2) * (2**n) + 1
    if sympy.isprime(q):
        print(q)
    n += 1

cp's OEIS Frontend

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

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