A079186 -id:A079186 - cp's OEIS frontend

A002489 a(n) = n^(n^2), or (n^n)^n.

1, 1, 16, 19683, 4294967296, 298023223876953125, 10314424798490535546171949056, 256923577521058878088611477224235621321607, 6277101735386680763835789423207666416102355444464034512896, 196627050475552913618075908526912116283103450944214766927315415537966391196809

Offset: 0

N. J. A. Sloane

The number of closed binary operations on a set of order n. Labeled groupoids.
The values of "googol" in base N: "10^100" in base 2 is 2^4=16; "10^100" in base 3 is 3^9=19683, etc. This is N^^3 by the "lower-valued" (left-associative) definition of the hyper4 or tetration operator (see Munafo webpage). - Robert Munafo, Jan 25 2010
n^(n^k) = (((n^n)^n)^...)^n, with k+1 n's, k >= 0. - Daniel Forgues, May 18 2013

			a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683.

John S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 6.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Michael Lee, Table of n, a(n) for n = 0..26 (first 16 terms from Vincenzo Librandi)
Robert Munafo, Hyper4 Iterated Exponential Function [From _Robert Munafo_, Jan 25 2010]
Eric Postpischil, Posting to sci.math newsgroup, May 21 1990.
P. Rossier, Grands nombres, Elemente der Mathematik, Vol. 3 (1948), p. 20; alternative link.
Index entries for sequences related to groupoids

a(n) = A079172(n) + A023814(n) = A079176(n) + A079179(n);
a(n) = A079182(n) + A023813(n) = A079186(n) + A079189(n);
a(n) = A079192(n) + A079195(n) + A079198(n) + A023815(n).
Cf. A002488, A001329, A002488, A023813, A076113, A090588, A000312, A258102.

[n^(n^2): n in [0..10]]; // Vincenzo Librandi, May 13 2011

Join[{1},Table[n^n^2,{n,10}]] (* Harvey P. Dale, Sep 06 2011 *)

a(n)=n^(n^2) \\ Charles R Greathouse IV, Nov 20 2012

a(n) = [x^(n^2)] 1/(1 - n*x). - Ilya Gutkovskiy, Oct 10 2017

Sum_{n>=1} 1/a(n) = A258102. - Amiram Eldar, Nov 11 2020

A079187 Number of isomorphism classes of non-anti-commutative closed binary operations (groupoids) on a set of order n.

Original entry on oeis.org

1, 4, 2334, 147124304, 2216860823492185, 13395780829563177947362200, 48974776899548402559651008669035131863, 151979850442580207421627199010701131897617064179661376, 534046142973031436667769900555231150876473571233474760878454735694121879

Offset: 1

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

nonn

Each a(n) is equal to the sum of the elements in row n of A079188.

C. van den Bosch, Closed binary operations on small sets
Index entries for sequences related to groupoids

Cf. A079186, A079188, A079190.

a(n) = A001329(n) - A079190(n), n > 1.

Edited, corrected and extended by Christian G. Bower, Dec 12 2003

a(9) from Sean A. Irvine, Aug 03 2025

A079189 Number of anti-commutative closed binary operations (groupoids) on a set of order n.

Original entry on oeis.org

1, 1, 8, 5832, 764411904, 32000000000000000, 669462604992000000000000000, 10090701947420325348336258984797490118656, 149274165541848061518941637595308945760198454444667437056, 2832386113499265897149023834314938475799908379160975581551362823935905234944

Offset: 0

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..20
C. van den Bosch, Closed binary operations on small sets
Index entries for sequences related to groupoids

Cf. A023813, A079186, A079190 (isomorphism classes), A079191, A079210.

a(n) = (n^n)*((n^2-n)^((n^2-n)/2)) \\ Andrew Howroyd, Jan 23 2022

a(n) = (n^n)*((n^2-n)^((n^2-n)/2)).
a(n) = A002489(n) - A079186(n).
a(n) = Sum_{k>=1} A079191(n,k)*A079210(n,k).
a(n) = A023813(n)*A023813(n-1).

Edited and extended by Christian G. Bower, Dec 12 2003

a(0)=1 prepended, a(8) corrected and a(9) added by Andrew Howroyd, Jan 23 2022

A079188 Number of isomorphism classes of non-anti-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 4, 1, 4, 44, 2285, 0, 0, 0, 24, 64, 212, 35240, 147088764

Offset: 1

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
A079176(n) is equal to the sum of the products of each element in row n of this sequence and the corresponding element of A079210.
The sum of each row n of this sequence is given by A079177(n).

			First four rows:
  0;
  0, 4;
  1, 4, 44, 2285;
  0, 0, 0, 24, 64, 212, 35240, 147088764.

C. van den Bosch, Closed binary operations on small sets
Index entries for sequences related to groupoids

Cf. A027423, A079171, A079186, A079187, A079191.

a(n) = A079171(n) - A079191(n).

cp's OEIS Frontend

A002489 a(n) = n^(n^2), or (n^n)^n.

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A079187 Number of isomorphism classes of non-anti-commutative closed binary operations (groupoids) on a set of order n.

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Formula

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A079189 Number of anti-commutative closed binary operations (groupoids) on a set of order n.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

Extensions

A079188 Number of isomorphism classes of non-anti-commutative closed binary operations on a set of order n, listed by class size.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula