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

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

Offset

1,2

Comments

a(n) is the number of relations on a set with n elements that are not one-to-one 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;
a(2) = 2^(2^2) - 2! =  14;
a(3) = 2^(3^2) - 3! = 506.

Mathematica

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

Crossrefs

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

Sequence in context: A024299 A190999 A320288 * A233014 A209096 A159645

Adjacent sequences: A344111 A344112 A344113 * A344115 A344116 A344117

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jun 04 2021

Status

approved