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COMMENTS
| 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.
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