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%I #19 Feb 05 2022 17:12:45
%S 1,1,2,8,39,235,1644,13152,118368,1183681,13020490,156245880,
%T 2031196439,28436750147,426551252206,6824820035296,116021940600031,
%U 2088394930800558,39679503685210601,793590073704212020
%N a(n) = n!*Sum_{k=1..n} mu(k)/k!, where mu(k) is the Moebius function.
%C Eigensequence of a triangle with mu(k) as the left border, the natural numbers (1, 2, 3, ...) as the right border; and the rest zeros. - _Gary W. Adamson_, Aug 01 2016
%C a(450) has 1000 decimal digits. - _Michael De Vlieger_, Aug 01 2016
%H Michael De Vlieger, <a href="/A068107/b068107.txt">Table of n, a(n) for n = 1..450</a>
%e The Moebius function (A008683) starts 1, -1, -1, 0, -1, so the sum in the definition is mu(1)/1! + mu(2)/2! + mu(3)/3! + mu(4)/4! + mu(5)/5! = 1/1 - 1/2 - 1/6 + 0/24 - 1/120 = 13/40. So a(5) = 5! * (13/40) = 39. - _Michael B. Porter_, Aug 02 2016
%t Table[n! Sum[MoebiusMu[k]/k!, {k, n}], {n, 20}] (* or *)
%t Flatten@ MapIndexed[#2! #1 &, Accumulate@ Table[MoebiusMu[k]/k!, {k, 450}]] (* useful for n > 1000, _Michael De Vlieger_, Aug 01 2016 *)
%Y Cf. A008683.
%K nonn
%O 1,3
%A _Leroy Quet_, Mar 22 2002
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