A076630 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.

1, 2, 5, 63, 1575297, 15398261127422599513389116979

Offset: 1

Author

Henry Bottomley, Oct 22 2002

Keywords

• nonn

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.

Examples

			a(4)=1+floor[5^4/(1*2*5)]=1+floor[62.5]=63.
		

Crossrefs

Cf. A076483.

Formula

a(n) = 1 + floor[a(n-1)^n / Product_i{0

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