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 A058922 a(n) = n*2^n - 2^n. 9
 0, 4, 16, 48, 128, 320, 768, 1792, 4096, 9216, 20480, 45056, 98304, 212992, 458752, 983040, 2097152, 4456448, 9437184, 19922944, 41943040, 88080384, 184549376, 385875968, 805306368, 1677721600, 3489660928, 7247757312 (list; graph; refs; listen; history; text; internal format)
 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 A001787(n) = a(n+1)/4. A073346(n, n-2) = a(n-2). Cf. A000337. - Omar E. Pol, Feb 22 2010 Sequence in context: A210066 A131126 A159964 * A215723 A034918 A119003 Adjacent sequences: A058919 A058920 A058921 * A058923 A058924 A058925 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 12 2001 STATUS approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)