%I A016123
%S A016123 1,12,133,1464,16105,177156,1948717,21435888,235794769,
%T A016123 2593742460,28531167061,313842837672,3452271214393,37974983358324,
%U A016123 417724816941565,4594972986357216,50544702849929377,555991731349223148
%N A016123 Expansion of 1/((1-x)(1-11x)).
%C A016123 11^a(n) is highest power of 11 dividing (11^(n+1))!.
%C A016123 Partial sums of powers of 11 (A001020).
%C A016123 a(n)=[(11^n)-1]/10 - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Feb 
               18 2008
%H A016123 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Link to a section of The World of Mathematics.</a>
%F A016123 a(n)= sum(11^k, k=0..n) = (11^(n+1)-1)/10.
%F A016123 G.f.: (1/(1-11*x)-1/(1-x))/(10*x)=1/((1-11*x)*(1-x)).
%F A016123 For analogues with primes 2, 3, 5, 7, 13 and 17 see: A000225, A003462, 
               A003463, A023000, A091030 and A091045, respectively.
%p A016123 a:=n->sum(11^(n-j),j=1..n): seq(a(n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%o A016123 (Other) sage: [lucas_number1(n,12,11) for n in xrange(1, 19)]# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
%o A016123 (Other) sage: [gaussian_binomial(n,1,11) for n in xrange(1,19)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A016123 Sequence in context: A003954 A120673 A120674 this_sequence A015457 A015469 
               A144785
%Y A016123 Adjacent sequences: A016120 A016121 A016122 this_sequence A016124 A016125 
               A016126
%K A016123 nonn
%O A016123 0,2
%A A016123 N. J. A. Sloane (njas(AT)research.att.com).