A362386 -id:A362386 - cp's OEIS frontend

A362385 Number of nonisomorphic magmas with n elements satisfying the equation x(yz) = xy.

1, 1, 3, 14, 197, 6139, 603933, 199410617

Offset: 0

Andrew Howroyd, Apr 24 2023

Cf. A001329 (magmas), A361720, A362382, A362384, A362386 (labeled case).

A362643 Number of labeled magmas with n elements satisfying the equations (xy)y = x and x(yz) = xy.

1, 1, 2, 10, 94, 1636, 49636, 2489824, 204626528, 27296455456, 5930440245856, 2144594499551296, 1333437360189448768, 1510196144261999035648, 3333925936841219018864384, 15357830414682103475484461056, 155003843551785210349182746546176

Offset: 0

Andrew Howroyd, Apr 28 2023

nonn

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

Cf. A000085, A362383, A362386, A362642 (isomorphism classes).

B(n, k)=my(p=serlaplace(exp(x + x^2/2 + O(x*x^n)))); sum(j=0, n, polcoef(p,j)^k*x^j/j!, O(x*x^n))
seq(n)=Vec(serlaplace(sum(k=0, n, log(B(n-k+1, k))^k/k!)))

E.g.f.: Sum_{k>=0} log(B(k,x))^k/k! where B(k,x) = Sum_{j>=0} A000085(j)^k*x^j/j!.

cp's OEIS Frontend

A362385 Number of nonisomorphic magmas with n elements satisfying the equation x(yz) = xy.

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A362643 Number of labeled magmas with n elements satisfying the equations (xy)y = x and x(yz) = xy.

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