A344114 a(n) = 2^(n^2) - n!.

1, 14, 506, 65512, 33554312, 68719476016, 562949953416272, 18446744073709511296, 2417851639229258349049472, 1267650600228229401496699576576, 2658455991569831745807614120520772352, 22300745198530623141535718272648361026978816, 748288838313422294120286634350736906063831234982912

Offset: 1

Author

Mohammad K. Azarian, Jun 04 2021

Keywords

• nonn
• easy

Comments

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

Examples

			a(1) = 2^(1^2) - 1! =   1;
a(2) = 2^(2^2) - 2! =  14;
a(3) = 2^(3^2) - 3! = 506.
		

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.

Crossrefs

Cf. A000312, A002416, A036679, A101030, A199656, A344110, A344112, A344113.

Programs

Mathematica

Table[2^(n^2) - n!, {n, 16}] // Flatten