A362386 Number of labeled magmas with n elements satisfying the equation x(yz) = xy.

1, 1, 4, 63, 3928, 671225, 415994376, 984103121743, 9271304662454080, 481332898418852452113, 104644384236229513639369600, 144227885665186612512723834972671, 914259315321600131058018257603156879616, 35436549344191965694685804548516417640353097545

Offset: 0

Author

Andrew Howroyd, Apr 25 2023

Keywords

• nonn

Examples

			One of the a(7) magmas is shown below. In this example there is a grouping {{1,2,3}, {4,5}, {6,7}}.
  x/y| 1 2 3 4 5 6 7
  ---+--------------
   1 | 1 1 1 2 2 3 3
   2 | 3 3 3 2 2 1 1
   3 | 3 3 3 1 1 3 3
   4 | 5 5 5 4 4 5 5
   5 | 4 4 4 4 4 5 5
   6 | 6 6 6 7 7 7 7
   7 | 6 6 6 7 7 6 6
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A362385 (isomorphism classes).

Programs

PARI

B(n,k)=log(sum(j=0, n, j^(j*k)*x^j/j!, O(x*x^n)))
seq(n)=Vec(serlaplace(sum(k=0, n, B(n-k+1,k)^k/k!)))

Formula

E.g.f.: Sum_{k>=0} log(B(k,x))^k/k! where B(k,x) = Sum_{j>=0} j^(j*k)*x^j/j!.