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A362386
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Number of labeled magmas with n elements satisfying the equation x(yz) = xy.
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3
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1, 1, 4, 63, 3928, 671225, 415994376, 984103121743, 9271304662454080, 481332898418852452113, 104644384236229513639369600, 144227885665186612512723834972671, 914259315321600131058018257603156879616, 35436549344191965694685804548516417640353097545
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OFFSET
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0,3
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LINKS
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FORMULA
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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!.
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EXAMPLE
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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
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PROG
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(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!)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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