OFFSET
1,2
COMMENTS
A hierarchical sequence (S(W'2{2}*c) - see A059126).
a(n) = -det(M(n+1)) where M(n) is the n X n matrix with m(i,i)=1, m(i,j)=-i/j for i != j. - Benoit Cloitre, Feb 01 2003
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..200
Jonas Wallgren, Hierarchical sequences, 2001.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
FORMULA
With offset 0, this is 4n*2^(n-1), the binomial transform of 4n. - Paul Barry, May 20 2003
a(1)=0, a(n) = 2*a(n-1) + 2^n for n>1. - Philippe Deléham, Apr 20 2009
a(n) = A000337(n) - 1. - Omar E. Pol, Feb 22 2010
From R. J. Mathar, Mar 01 2010: (Start)
a(n)= 4*a(n-1) - 4*a(n-2).
G.f.: 4*x^2/(2*x-1)^2. (End)
From Amiram Eldar, Jan 12 2021: (Start)
Sum_{n>=2} 1/a(n) = log(2)/2.
Sum_{n>=2} (-1)^n/a(n) = log(3/2)/2. (End)
MATHEMATICA
Table[n*2^n-2^n, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 15 2011 *)
PROG
(PARI) { for (n = 1, 200, write("b058922.txt", n, " ", n*2^n - 2^n); ) } \\ Harry J. Smith, Jun 24 2009
(Haskell)
a058922 n = (n - 1) * 2 ^ n
a058922_list = zipWith (*) [0..] $ tail a000079_list
-- Reinhard Zumkeller, Jul 11 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 12 2001
STATUS
approved