%I A091045
%S A091045 1,18,307,5220,88741,1508598,25646167,435984840,7411742281,125999618778,
%T A091045 2141993519227,36413889826860,619036127056621,10523614159962558,
%U A091045 178901440719363487,3041324492229179280,51702516367896047761
%N A091045 Partial sums of powers of 17 (A001026).
%C A091045 17^a(n) is highest power of 17 dividing (17^n)!.
%F A091045 a(n)= sum(17^k, k=0..n-1) = (17^n-1)/16.
%F A091045 G.f.: x/((1-17*x)*(1-x))= (1/(1-17*x) - 1/(1-x))/16.
%F A091045 For analogues with primes 2, 3, 5, 7, 11, 13, ... see: A000225, A003462, 
               A003463, A023000, A016123, A091030, ...
%F A091045 a(n)=17*a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Oct 29 2009]
%e A091045 For n=2, a(2)=17*1+1=18; n=3, a(3)=17*18+1=307; n=4, a(4)=17*307+1=5220 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]
%o A091045 (Other) sage: [gaussian_binomial(n,1,17) for n in xrange(1,18)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A091045 Sequence in context: A170651 A170699 A170737 this_sequence A158532 A171323 
               A049660
%Y A091045 Adjacent sequences: A091042 A091043 A091044 this_sequence A091046 A091047 
               A091048
%K A091045 nonn,easy
%O A091045 1,2
%A A091045 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Jan 23 2004