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Cf. A090683.
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reviewed
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O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, Springer, 2009, pages 58-62.
Number of Green's H-classes in the full transformation semigroup on [n]. Row sums of A090683. - Geoffrey Critzer, Dec 27 2022
Wikipedia, <a href="http://en.wikipedia.org/wiki/Green's_relations">Green's relations</a>
Wikipedia, <a href="http://en.wikipedia.org/wiki/Transformation_semigroup">Transformation semigroup</a>
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(MAGMAMagma) [(&+[Binomial(n, k)*StirlingSecond(n, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Feb 07 2019