A176787 -id:A176787 - cp's OEIS frontend

A176788 a(n) = (0!! + 1!! + 2!! + 3!! + ... + (n-1)!!) mod n.

0, 0, 1, 3, 0, 0, 1, 7, 0, 2, 6, 3, 12, 10, 12, 3, 13, 6, 11, 7, 3, 8, 14, 15, 12, 22, 15, 3, 19, 12, 16, 11, 30, 14, 17, 15, 17, 34, 9, 7, 26, 24, 36, 19, 42, 8, 2, 3, 24, 12, 48, 35, 2, 42, 52, 31, 15, 22, 51, 27, 32, 56, 24, 27, 22, 30, 6, 31, 54, 52, 12, 15, 7, 56, 12, 15, 52, 48

Offset: 1

Paolo P. Lava & Giorgio Balzarotti, Apr 26 2010

			0!! mod 1 = 1 mod 1 = 0.
(0!!+1!!) mod 2 = (1 + 1) mod 2 = 0.
(0!!+1!!+2!!) mod 3 = (1 + 1 + 2) mod 3 = 1.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A049782, A176787, A176789.

A176788 := proc(n)
        A129981(n-1) mod n ;
end proc: # R. J. Mathar, Jul 13 2012

Table[Mod[Total[Range[0,n-1]!!],n],{n,80}] (* Harvey P. Dale, Nov 15 2021 *)

a(n) = A129981(n-1) mod n.

A176789 a(n) = (0!! - 1!! + 2!! - 3!! + ... + (-1)^(n-1)*(n-1)!!) mod n.

Original entry on oeis.org

0, 0, 2, 3, 2, 4, 5, 7, 4, 4, 2, 7, 3, 0, 4, 3, 5, 10, 3, 19, 7, 4, 3, 7, 14, 0, 10, 7, 5, 4, 29, 11, 4, 6, 14, 19, 4, 26, 13, 39, 13, 28, 2, 15, 19, 20, 11, 19, 14, 14, 40, 39, 0, 10, 4, 7, 7, 8, 7, 19, 26, 38, 28, 27, 39, 4, 57, 23, 43, 14, 5, 55, 30, 6, 64, 7, 70, 52, 50, 19, 37, 10, 75, 7

Offset: 1

Paolo P. Lava & Giorgio Balzarotti, Apr 26 2010

Alternating sum of double factorials modulo n.

			a(1) = 0!! mod 1 = 1 mod 1 = 0.
a(2) = (0!! - 1!!) mod 2 = (1 - 1) mod 2 = 0.
a(3) = (0!! - 1!! + 2!!) mod 3 = (1 - 1 + 2) mod 3 = 2.

Cf. A049782, A176787, A176788.

A176789 := proc(n)
        modp(1-(-1)^n*A129831(n-1), n) ;
end proc: # R. J. Mathar, Aug 22 2012

Table[Mod[Sum[(-1)^k k!!,{k,0,n-1}],n],{n,90}] (* Harvey P. Dale, Dec 08 2012 *)

a(n) = (Sum_{k=0..n-1} (-1)^k*k!!) mod n = (1 + (-1)^(n-1)*A129831(n-1)) mod n.

cp's OEIS Frontend

A176788 a(n) = (0!! + 1!! + 2!! + 3!! + ... + (n-1)!!) mod n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula