A068107 a(n) = n!*Sum_{k=1..n} mu(k)/k!, where mu(k) is the Moebius function.

1, 1, 2, 8, 39, 235, 1644, 13152, 118368, 1183681, 13020490, 156245880, 2031196439, 28436750147, 426551252206, 6824820035296, 116021940600031, 2088394930800558, 39679503685210601, 793590073704212020

Offset: 1

Author

Leroy Quet, Mar 22 2002

Keywords

• nonn

Comments

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

a(450) has 1000 decimal digits. - Michael De Vlieger, Aug 01 2016

Examples

			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
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A008683.

Programs

Mathematica

Table[n! Sum[MoebiusMu[k]/k!, {k, n}], {n, 20}] (* or *)
Flatten@ MapIndexed[#2! #1 &, Accumulate@ Table[MoebiusMu[k]/k!, {k, 450}]] (* useful for n > 1000, Michael De Vlieger, Aug 01 2016 *)