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A061301 a(n) = 2^(n*2^(n-1)). 4
1, 2, 16, 4096, 4294967296, 1208925819614629174706176, 6277101735386680763835789423207666416102355444464034512896 (list; graph; refs; listen; history; text; internal format)
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 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

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), 231-245.

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^(n-1)*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 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

MATHEMATICA

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

PROG

(MAGMA) [2^(n*2^(n-1)): 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)my-deja.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

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Last modified August 1 07:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)