%I A091030
%S A091030 1,14,183,2380,30941,402234,5229043,67977560,883708281,11488207654,
%T A091030 149346699503,1941507093540,25239592216021,328114698808274,
%U A091030 4265491084507563,55451384098598320,720867993281778161
%N A091030 Partial sums of powers of 13 (A001022).
%C A091030 13^a(n) is highest power of 13 dividing (13^n)!.
%F A091030 a(n)= sum(13^k, k=0..n-1) = (13^n-1)/12.
%F A091030 G.f.: x/((1-13*x)*(1-x))= (1/(1-13*x) - 1/(1-x))/12.
%F A091030 For analogues with primes 2, 3, 5, 7 and 11 see A000225, A003462, A003463, 
               A023000 and A016123 respectively.
%p A091030 a:=n->sum(13^(n-j),j=1..n): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%o A091030 (Other) sage: [gaussian_binomial(n,1,13) for n in xrange(1,18)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A091030 Cf. A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, 
               A016123, A016125.
%Y A091030 Sequence in context: A163416 A097828 A030008 this_sequence A165152 A055759 
               A086946
%Y A091030 Adjacent sequences: A091027 A091028 A091029 this_sequence A091031 A091032 
               A091033
%K A091030 nonn,easy
%O A091030 1,2
%A A091030 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Jan 23 2004