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A120368
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a(n) = number of sequences (a_1, a_2, ..., a_n) in {1,2,...,n} such that the range {a_1, a_2, ..., a_n} is an interval.
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0
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1, 1, 4, 21, 142, 1175, 11476, 129073, 1641802, 23292459, 364530688, 6237123365, 115806988342, 2318774566303, 49799220552940, 1141845310143897, 27838573420105762, 719091858410591507, 19617132273844278232
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = (n+1)*A(n) - (A(n+1)-A(n))/2, where A is sequence A000670
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FORMULA
| Exponential generating function = (3-2*exp(x)+x*exp(x))/(exp(x)-2)^2 formula: a(0)=1, a(n)=Sum_{k=1..n}(n-k+1)*k!*Stirling2(n,k)
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EXAMPLE
| the range of (2,5,5,3,4) is the interval {2,3,4,5}, the range of (2,5,5,3,2) is {2,3,5}, not an interval since 4 is missing
a(3) = 21 because the only 3-sequences in {1,2,3} (from a total of 3^3=27) whose range is not an interval are (1,1,3), (1,3,1), (1,3,3), (3,1,1), (3,1,3) and (3,3,1)
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CROSSREFS
| Sequence in context: A121124 A180399 A087761 * A053482 A158577 A006879
Adjacent sequences: A120365 A120366 A120367 * A120369 A120370 A120371
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KEYWORD
| easy,nonn
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AUTHOR
| Jose Luis Arregui (arregui(AT)unizar.es), Jun 26 2006
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