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%I #9 Oct 19 2014 06:18:10
%S 2,9,2,4,9,9,2,7,8,7,4,3,1,2,8,5,5,1,4,5,0,0,1,5,6,0,9,4,1,7,4,4,2,4,
%T 0,1,3,2,8,9,9,8,3,9,3,1,0,2,2,9,3,1,2,1,8,0,5,0,9,4,1,3,2,9,6,8,6,9,
%U 2,5,8,8,3,7,3,3,9,2,4,9,3,5,3,5,4,7
%N Decimal expansion of sum_{n >= 1} n!/p(n), where p(n) = [n/1]!*[n/2]!*...*[n/n]!, and [ ] = floor.
%C Let t(n) = n!/p(n). Then t(n) is an integer for n = 1..15, and max{t(n), n = 1..infinity}} = t(23) = 77452.802... . It appears that t(n) < 1/10 for n > 35 and t(n) < 10^(-6) for n > 45.
%e 292499.27874312855145001560941744240132899839310229312180509413296869258837339...
%p evalf(sum(n!/product(floor(n/k)!, k=2..n), n=1..infinity), 120); # _Vaclav Kotesovec_, Oct 19 2014
%t u = N[Sum[n!/Product[Floor[n/k]!, {k, 2, n}], {n, 1, 200}], 130]
%t RealDigits[u] (* A248695 *)
%Y Cf. A214869, A248696.
%K nonn,easy,cons
%O 6,1
%A _Clark Kimberling_, Oct 13 2014
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