cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A079182 Number of non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 8, 18954, 4293918720, 298023193359375000, 10314424798468598595531571200, 256923577521058877628624940679495660344806, 6277101735386680763835789098689112757675628661308013936640
Offset: 1

Views

Author

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

Keywords

Comments

A023813(n) + A079182(n) = A002489(n).
Each a(n) is equal to the sum of the products of each element in row n of A079184 and the corresponding element of A079210.

Links

Crossrefs

Cf. A023813, A079178, A079180.

Programs

  • Mathematica
    Table[n^(n^2)-n^((n^2+n)/2), {n,1,10}] (* Geoffrey Critzer, Jan 27 2013 *)

Formula

a(n) = n^(n^2)-n^((n^2-n)/2).

Extensions

More terms from Geoffrey Critzer, Jan 27 2013

A079183 Number of isomorphism classes of non-commutative closed binary operations (groupoids) on a set of order n.

Original entry on oeis.org

0, 6, 3201, 178937984, 2483527282664925, 14325590003288422852104768, 50976900301814583996024242298024434780, 155682086691137947272042494203068030678979503481450216
Offset: 1

Views

Author

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

Keywords

Comments

Each a(n) is equal to the sum of the elements in row n of A079184.

Links

Crossrefs

Cf. A001329, A001425, A079184.

Formula

a(n) = A001329(n) - A001425(n).

Extensions

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

A079185 Number of isomorphism classes of commutative closed binary operations (groupoids) on a set of order n, listed by class size.

Original entry on oeis.org

1, 0, 4, 1, 4, 8, 116, 0, 0, 0, 8, 0, 28, 504, 43428
Offset: 1

Views

Author

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

Keywords

Comments

A079184(n)+A079185(n)=A079171(n).
Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
First four rows: 1; 0,4; 1,4,8,116; 0,0,0,8,0,28,504,43428
A079176(x) is equal to the sum of the products of each element in row x of this sequence and the corresponding element of A079210.
The sum of each row n is given by A079177(n).

Links

Crossrefs

Cf. A001425, A023183, A079184. a(n, A027423(n)) = A030255(n).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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