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A023997
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Number of block permutations on an n-set.
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6
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1, 1, 3, 25, 339, 6721, 179643, 6166105, 262308819, 13471274401, 818288740923, 57836113793305, 4693153430067699, 432360767273547841, 44794795522199781243, 5176959027946049635225, 662704551840482536170579
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A block permutation of a set X is a bijection between two quotient sets of X (of necessarily equal rank).
Number of labeled partitions of (n,n) into pairs (i,j) where there are n black objects labeled 1..n and n white objects labeled 1..n. Each partition must have at least one black object and at least one white object. - Christian G. Bower, Jun 03 2005
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REFERENCES
| D. G. FitzGerald and Jonathan Leech, Dual symmetric inverse monoids and representation theory, J. Australian Mathematical Society (Series A), Vol. 64 (1998), pp. 345-367.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..45
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FORMULA
| a(0)=1, a(n) = Sum_(k=1..n)_ (k!(S_n, k_)^2), S_n, k_ = Stirling number of 2nd kind.
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EXAMPLE
| For n=3, there are the 3! ordinary permutations (of rank 3), 18 block permutations of rank 2 (2! for each pair of partitions of rank 2) and the single rank 1 one.
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MATHEMATICA
| Table[Sum[StirlingS2[n, k]^2k!, {k, 0, n}], {n, 0, 100}] [Emanuele Munarini, Jul 04 2011]
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PROG
| (Maxima) makelist(sum(stirling2(n, k)^2*k!, k, 0, n), n, 0, 24); [Emanuele Munarini, Jul 04 2011]
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CROSSREFS
| Cf. A023998, A002720, A014235, A111420.
Sequence in context: A001907 A181085 A143635 * A154961 A085527 A093360
Adjacent sequences: A023994 A023995 A023996 * A023998 A023999 A024000
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Des FitzGerald (D.FitzGerald(AT)utas.edu.au)
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net), Jun 03 2005
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