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Search: id:A124426
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| A124426 |
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Product of two successive Bell numbers. |
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+0
1
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| 1, 2, 10, 75, 780, 10556, 178031, 3630780, 87548580, 2452523325, 78697155750, 2859220516290, 116482516809889, 5277304280371714, 264005848594606490, 14493602135008296115, 868435614538568029188, 56520205738693680322836
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of partitions of the set {1,2,...,2n+1} having no blocks that contain both odd and even entries. Example: a(2)=10 because we have 135|24, 15|24|3, 1|24|35, 135|2|4, 15|2|3|4, 1|2|35|4, 13|24|5, 1|24|3|5, 13|2|4|5 and 1|2|3|4|5. a(n)=A124419(2n+1)=A124418(2n+1,0).
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FORMULA
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a(n)=B(n)B(n+1), where B(q) are the Bell numbers (A000110), i.e. B(n)=Sum(S2(n,k),k=1..n), S2(n,k) being the Stirling numbers of the 2nd kind (A008277).
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MAPLE
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with(combinat): seq(bell(n)*bell(n+1), n=0..19);
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CROSSREFS
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Cf. A000110, A008277, A124418, A124419.
Sequence in context: A059104 A094071 A136222 this_sequence A066223 A088500 A095789
Adjacent sequences: A124423 A124424 A124425 this_sequence A124427 A124428 A124429
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch and Paul D. Hanna (deutsch(AT)duke.poly.edu; pauldhanna(AT)juno.com), Nov 03 2006
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