%I A083420
%S A083420 1,7,31,127,511,2047,8191,32767,131071,524287,2097151,8388607,33554431,
%T A083420 134217727,536870911,2147483647,8589934591,34359738367,137438953471,
%U A083420 549755813887,2199023255551,8796093022207,35184372088831
%N A083420 a(n)=2*4^n-1.
%C A083420 Sum of divisors of 4^n. - Paul Barry (pbarry(AT)wit.ie), Oct 13 2005
%C A083420 a(n) = A099393(n) + A020522(n) = A000302(n) + A024036(n). - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 07 2006
%C A083420 Subsequence of A000069; A132680(a(n)) = A005408(n). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Aug 26 2007
%H A083420 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A083420 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Rule220.html">Rule 220</a>
%F A083420 G.f. (1+2x)/((1-x)(1-4x)) E.g.f. 2exp(4x)-exp(x)
%F A083420 With a leading zero, this is a(n)=(4^n-2+0^n)/2, the binomial transform 
               of A080925. - Paul Barry (pbarry(AT)wit.ie), May 19 2003
%F A083420 a(n) = (-16^n/2)*B(2n, 1/4)/B(2n) where B(n, x) is the n-th Bernoulli 
               polynomial and B(k)=B(k, 0) is the k-th Bernoulli number. a(n)=5*a(n-1)-4*a(n-2). 
               Also a(n) = (-4^n/2)*B(2n, 1/2)/B(2n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 18 2004
%p A083420 [seq (stirling2(2*n,2),n=1..23)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 06 2006
%t A083420 Table[ChebyshevT[2,2^n],{n,1,40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Nov 03 2009]
%Y A083420 Cf. A083421.
%Y A083420 Sequence in context: A153005 A056909 A002147 this_sequence A036282 A033474 
               A001896
%Y A083420 Adjacent sequences: A083417 A083418 A083419 this_sequence A083421 A083422 
               A083423
%K A083420 easy,nonn
%O A083420 0,2
%A A083420 Paul Barry (pbarry(AT)wit.ie), Apr 29 2003