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A068199
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One of a family of sequences that interpolates between the Bell numbers and the factorials.
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3
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1, 2, 6, 24, 114, 618, 3732, 24702, 177126, 1363740, 11195286, 97437138, 894857712, 8637708858, 87333790686, 922203924216, 10144109299146, 115972625504994, 1375221840671220, 16884112119546534, 214270296662325534
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. Labelle et al., Stirling numbers interpolation using permutations with forbidden subsequences, Discrete Math. 246 (2002), 177-195.
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FORMULA
| E.g.f.: 1 + 2exp(3exp(x)-3).
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MAPLE
| g:= proc(n) option remember; `if` (n=0, 1, (1+add (binomial (n-1, k-1) *g(n-k), k=1..n-1)) *3) end: a:= n-> `if`(n=0, 1, 2*g(n-1)): seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
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CROSSREFS
| Cf. A000110, A001861, this, A068200, A068201, ..., A000142.
Equals 2 * A027710(n).
Sequence in context: A054872 A134664 A171448 * A189846 A189283 A177522
Adjacent sequences: A068196 A068197 A068198 * A068200 A068201 A068202
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 23 2002
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008
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