A061301 a(n) = 2^(n*2^(n-1)).

1, 2, 16, 4096, 4294967296, 1208925819614629174706176, 6277101735386680763835789423207666416102355444464034512896

Offset: 0

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 05 2001

Keywords

• nonn
• easy

Comments

Determinant of character table of elementary Abelian group (C_2)^n.

a(7) has 135 digits. - Jason Earls, Jun 11 2001

Number of functions f:2^X->2^X where X is an n-element set such that f(A) is a subset of A for all A in 2^X (where 2^X denotes the power set of X). - W. Edwin Clark, Nov 06 2003

Examples

			a(2) = 16 because the character table for C_2 X C_2 is / 1 1 1 1 / 1 -1 -1 1 / 1 -1 1 -1 / 1 1-1 -1 / with determinant 16 = (2^2)^(2^1).
a(1) = 2 since 2^{1} = { {}, {1}} and the functions f : 2^{1}->2^{1} satisfying f(A) is a subset of A for all A are g and h where g({})={}, g({1})={} and h({}) = {}, h({1})={1}. - _W. Edwin Clark_, Nov 06 2003
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..9
• Nate Chenette, Reed Phillips, Lara Pudwell, and Manda Riehl, Occurrences of reciprocal sign epistasis in single-and multi-peaked theoretical fitness landscapes, Rose-Hulman and Valparaiso Universities (2022).
• F. Echenique, Counting Combinatorial Choice Rules, Games and Economic Behavior, Vol. 58, No. 2 (2007), 231-245.
• Lara Pudwell, Nathan Chenette, and Manda Riehl, Statistics on Hypercube Orientations, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020).

Crossrefs

Cf. A088322.

Programs

Magma

[2^(n*2^(n-1)): n in [0..5]]; // Vincenzo Librandi, Sep 02 2018

Mathematica

Table[2^(n 2^(n - 1)), {n, 0, 7}] (* Vincenzo Librandi, Sep 02 2018 *)

Formula

a(n) = 2^Sum_{i=0..n} i*binomial(n, i) = 2^(2^(n-1)*n). - W. Edwin Clark, Nov 06 2003

Extensions

More terms from Jason Earls, Jun 11 2001

Edited by N. J. A. Sloane, Oct 27 2008 at the suggestion of R. J. Mathar

Offset changed to 0 by Vincenzo Librandi, Sep 02 2018