A258817 a(n) = (!0 + !1 +... + !(n-1)) mod n.

0, 1, 2, 0, 3, 3, 0, 0, 8, 5, 4, 0, 9, 7, 8, 0, 13, 9, 4, 0, 14, 11, 14, 0, 3, 13, 17, 0, 25, 15, 4, 0, 26, 17, 28, 0, 30, 19, 35, 0, 4, 21, 9, 0, 8, 23, 32, 0, 7, 25, 47, 0, 30, 27, 48, 0, 23, 29, 45, 0, 48, 31, 35, 0, 48, 33, 12, 0, 14, 35, 7, 0, 34, 37, 53

Offset: 1

Author

Michel Lagneau, Jun 11 2015

Keywords

• nonn

Comments

!n is a subfactorial number (A000166).

Property of the sequence: a(1) = a(7) = 0 and a(4k) = 0 for k=1,2,...

Examples

			a(5)= 3 because !0 + !1 + !2 + !3 + !4 = 1 + 0 + 1 + 2 + 9 = 13 == 3 mod 5.
		

Crossrefs

Cf. A000166, A173184.

Programs

Maple

A:= proc(n) option remember; if n<=1 then 1-n else (n-1)*(procname(n-1)+procname(n-2)); fi; end;
a:=n->n!*sum((-1)^k/k!, k=0..n):
lf:=n->add(A(k), k=0..n-1);[seq(lf(n) mod n, n=1..40)];

Mathematica

Table[Mod[Total[Subfactorial[Range[0, n-1]]], n], {n, Range[80]}]

Formula

a(n)= A173184(n) mod n.