A362643 - OEIS

%I #7 Apr 30 2023 23:16:43

%S 1,1,2,10,94,1636,49636,2489824,204626528,27296455456,5930440245856,

%T 2144594499551296,1333437360189448768,1510196144261999035648,

%U 3333925936841219018864384,15357830414682103475484461056,155003843551785210349182746546176

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

%H Andrew Howroyd, <a href="/A362643/b362643.txt">Table of n, a(n) for n = 0..50</a>

%F 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!.

%o (PARI)

%o 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))

%o seq(n)=Vec(serlaplace(sum(k=0, n, log(B(n-k+1, k))^k/k!)))

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

%K nonn

%O 0,3

%A _Andrew Howroyd_, Apr 28 2023