A344113 a(n) = 2^(n^2) - n^n.

1, 12, 485, 65280, 33551307, 68719430080, 562949952597769, 18446744073692774400, 2417851639229257961991863, 1267650600228229401486703205376, 2658455991569831745807613835249018541, 22300745198530623141535718272639445405532160

Offset

1,2

Comments

a(n) is the number of relations on a set with n elements that are not functions.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..57

Mohammad K. Azarian, Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141.

Example

a(1) = 2^(1^2) - 1^1 = 1.
a(2) = 2^(2^2) - 2^2 = 12.
a(3) = 2^(3^2) - 3^3 = 485.

Mathematica

Table[2^(n^2) - n^n, {n, 12}] // Flatten

Crossrefs

Cf. A000312, A002416, A036679, A344110, A344112, A344114.

Sequence in context: A012394 A012686 A012466 * A229634 A196704 A175322

Adjacent sequences: A344110 A344111 A344112 * A344114 A344115 A344116

Keyword

nonn,easy

Author

Mohammad K. Azarian, May 14 2021

Status

approved