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%I #13 Sep 15 2024 02:47:12
%S 1,5,25,25,625,3125,15625,78125,78125,1953125,9765625,48828125,
%T 244140625,244140625,1220703125,6103515625,30517578125,152587890625,
%U 30517578125,3814697265625,19073486328125
%N Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/5.
%C Numerators are given under A121006. See A121006 for further comments.
%F a(n)=denominator(r(n)) with r(n) := rIII(p=1,n) = sum(((-1)^k)*C(k)/5^k,k=0..n) and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.
%e Rationals r(n): 1, 4/5, 22/25, 21/25, 539/625, 2653/3125, 13397/15625, 66556/78125, 66842/78125, 1666188/1953125, 8347736/9765625,...
%Y The second member (p=2) is A121008/A121009.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 16 2006