A057438 a(1) = 1; a(n+1) = (Product_{k = 1..n} [a(k)]) * (Sum_{j = 1..n} [1/a(j)]).
1, 1, 2, 5, 27, 739, 546391, 298543324411, 89128116550480609893151, 7943821159836055611643954282977557048699079331, 63104294619459055797454850600852928915607093463575707111291209057699988334565551829102647591
Offset: 1
Examples
a(5) = a(1)*a(2)*a(3)*a(4)*(1/a(1) + 1/a(2) + 1/a(3) + 1/a(4)) = 1*1*2*5*(1 + 1 + 1/2 + 1/5) = 27.
Programs
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Mathematica
a[1] = 1; a[n_] := a[n] = Sum[1/a[n - k], {k, n - 1}] Product[a[n - k], {k, n - 1}]; Table[ a[n], {n, 11}] (* Robert G. Wilson v, Jun 14 2005 *)
Formula
a(n) = a(n-1)^2+a(n-1)a(n-2)-a(n-2)^3 (valid for all n>3). - Ivan Sadofschi, Feb 22 2011
a(n) = a(n-1)^2+A074056(n-2) where A074056 is partial product of A057438. Close to a(n-1)^2+a(n-1)*0.365177806085453... and 1.1087260396143829635274191...^(2^n). - Henry Bottomley, Aug 14 2002
Extensions
More terms from Leroy Quet, Sep 08 2000
Comments