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

1,3

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A008683.

Sequence in context: A020047 A231496 A347665 * A308207 A307709 A217945

Adjacent sequences: A068104 A068105 A068106 * A068108 A068109 A068110

Keyword

nonn

Author

Leroy Quet, Mar 22 2002

Status

approved