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A060639
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Number of pairs of partitions of [n] whose join is the partition {{1,2,...,n}}.
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1
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1, 1, 3, 15, 119, 1343, 19905, 369113, 8285261, 219627683, 6746244739, 236561380795, 9356173080985, 413251604702069, 20215438754502217, 1087524296159855603, 63950948621703499839, 4089003767746536828183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| E. R. Canfield, Meet and join in the partition lattice, Electronic Journal of Combinatorics, 8 (2001) R15.
B. Pittel, Where the typical set partitions meet and join, Electronic Journal of Combinatorics, 7 (2000) R5.
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FORMULA
| The e.g.f. J(x) satisfies the equation Sum_{n=0}^{\infty} (B_n)^2 x^n/n! = exp(J(x)-1), where B_n is the n-th Bell number.
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EXAMPLE
| J(2) = 3 because there are two partitions of {1,2} and of the four pairs of partitions, only the pair ( {{1},{2}}, {{1},{2}} ) fails to have join {{1,2}}.
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CROSSREFS
| Bell numbers: A000110, Stirling numbers of the second kind: A000225, number of pairs whose meet equals {{1}, {2}, ..., {n}}: A059849.
Cf. A001188.
Sequence in context: A136654 A145161 A121422 * A068052 A068859 A006454
Adjacent sequences: A060636 A060637 A060638 * A060640 A060641 A060642
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KEYWORD
| nonn
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AUTHOR
| E. R. Canfield (erc(AT)cs.uga.edu), Apr 16 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 18 2001
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