

A061301


a(n) = 2^(n*2^(n1)).


4




OFFSET

0,2


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 nelement 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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..9
F. Echenique, Counting Combinatorial Choice Rules, Games and Economic Behavior, Vol. 58, No. 2 (2007), 231245.
Lara Pudwell, Nathan Chenette, Manda Riehl, Statistics on Hypercube Orientations, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020).


FORMULA

a(n) = 2^Sum_{i=0..n} i*binomial(n, i) = 2^(2^(n1)*n).  W. Edwin Clark, Nov 06 2003


EXAMPLE

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 11 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


MATHEMATICA

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


PROG

(MAGMA) [2^(n*2^(n1)): n in [0..5]]; // Vincenzo Librandi, Sep 02 2018


CROSSREFS

Cf. A088322.
Sequence in context: A270124 A138834 A088321 * A180962 A324565 A306729
Adjacent sequences: A061298 A061299 A061300 * A061302 A061303 A061304


KEYWORD

nonn,easy


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Jun 05 2001


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


STATUS

approved



