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%I #3 Mar 30 2012 18:51:39
%S 1,2,5,63,1575297,15398261127422599513389116979
%N a(n) is the smallest number such that product of first n terms is strictly greater than n-th power of a(n-1) starting with a(1)=1.
%C Next term is 1.343...*10^160. Of the n^n ways of selecting n terms from {a(1),a(2),...,a(n)}, n!*Sum_k{1<=k<=n}(k-1)^k/k!=A076483(n) ways have a product strictly less than a(1)*a(2)*...*a(n) and this is possibly the smallest sequence with that property. If the definition had been: a(n) is the smallest number such that sum of first n terms is greater than n times a(n-1) starting with a(1)=1, then the resulting sequence would have been A003422.
%F a(n) = 1 + floor[a(n-1)^n / Product_i{0<i<n}a(i)].
%e a(4)=1+floor[5^4/(1*2*5)]=1+floor[62.5]=63.
%Y Cf. A076483.
%K nonn
%O 1,2
%A _Henry Bottomley_, Oct 22 2002
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