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A362386 Number of labeled magmas with n elements satisfying the equation x(yz) = xy. 3
1, 1, 4, 63, 3928, 671225, 415994376, 984103121743, 9271304662454080, 481332898418852452113, 104644384236229513639369600, 144227885665186612512723834972671, 914259315321600131058018257603156879616, 35436549344191965694685804548516417640353097545 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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!.
EXAMPLE
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
PROG
(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!)))
CROSSREFS
Cf. A362385 (isomorphism classes).
Sequence in context: A203512 A354653 A213545 * A361683 A111444 A368111
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 25 2023
STATUS
approved

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Last modified July 24 10:37 EDT 2024. Contains 374583 sequences. (Running on oeis4.)