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A279644
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a(n) is the n-th term of the exponential transform of the n-th powers.
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5
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1, 1, 5, 52, 1445, 104116, 16379797, 6067246144, 5270005429705, 9832425683734288, 40944833826904310921, 384044953998005246634304, 7656468877618298485395299533, 332312769563869315072667521436992, 31885558406529826494376921134421228189
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OFFSET
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0,3
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COMMENTS
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Number of labeled magmas with n elements satisfying the equation x(yz) = xz. - Andrew Howroyd, Apr 24 2023
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LINKS
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FORMULA
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a(n) = n! * [x^n] exp(exp(x)*(Sum_{j=0..n} Stirling2(n,j)*x^j) - delta_{0,n}).
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MAPLE
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b:= proc(n, k) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1)*j^k*b(n-j, k), j=1..n))
end:
a:= n-> b(n$2):
seq(a(n), n=0..15);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Binomial[n-1, j-1]*j^k*b[n-j, k], {j, 1, n}]];
a[n_] := b[n, n];
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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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