cp's OEIS Frontend

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

%I A362386 #14 Apr 26 2023 10:28:34
%S A362386 1,1,4,63,3928,671225,415994376,984103121743,9271304662454080,
%T A362386 481332898418852452113,104644384236229513639369600,
%U A362386 144227885665186612512723834972671,914259315321600131058018257603156879616,35436549344191965694685804548516417640353097545
%N A362386 Number of labeled magmas with n elements satisfying the equation x(yz) = xy.
%H A362386 Andrew Howroyd, <a href="/A362386/b362386.txt">Table of n, a(n) for n = 0..50</a>
%F A362386 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!.
%e A362386 One of the a(7) magmas is shown below. In this example there is a grouping {{1,2,3}, {4,5}, {6,7}}.
%e A362386   x/y| 1 2 3 4 5 6 7
%e A362386   ---+--------------
%e A362386    1 | 1 1 1 2 2 3 3
%e A362386    2 | 3 3 3 2 2 1 1
%e A362386    3 | 3 3 3 1 1 3 3
%e A362386    4 | 5 5 5 4 4 5 5
%e A362386    5 | 4 4 4 4 4 5 5
%e A362386    6 | 6 6 6 7 7 7 7
%e A362386    7 | 6 6 6 7 7 6 6
%o A362386 (PARI)
%o A362386 B(n,k)=log(sum(j=0, n, j^(j*k)*x^j/j!, O(x*x^n)))
%o A362386 seq(n)=Vec(serlaplace(sum(k=0, n, B(n-k+1,k)^k/k!)))
%Y A362386 Cf. A362385 (isomorphism classes).
%K A362386 nonn
%O A362386 0,3
%A A362386 _Andrew Howroyd_, Apr 25 2023