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Search: id:A097900
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| A097900 |
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Number of runs of length 1 in all permutations of [n]. (The permutation 3574162 has two runs of length 1: 357/4/16/2). |
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3
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| 1, 2, 7, 32, 180, 1200, 9240, 80640, 786240, 8467200, 99792000, 1277337600, 17643225600, 261534873600, 4140968832000, 69742632960000, 1244905998336000, 23475370254336000, 466306218233856000, 9731608032706560000
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OFFSET
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1,2
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REFERENCES
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Ira. M. Gessel, Generating functions and enumeration of sequences, Ph. D. Thesis, MIT, 1977.
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FORMULA
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a(n)=n!(n+4)/6 for n>=2. E.g.f.= x(6-6x+x^2)/[6(1-x)^2].
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EXAMPLE
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a(3)=7 because there are 7 runs of length 1 in the permutations 123, 13(2),
(2)13, 23(1), (3)12, (3)(2)(1) (shown between parentheses).
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MAPLE
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1, seq(n!*(n+4)/6, n=2..23);
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CROSSREFS
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Sequence in context: A059439 A006014 A121555 this_sequence A000153 A006154 A000987
Adjacent sequences: A097897 A097898 A097899 this_sequence A097901 A097902 A097903
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ira Gessel (gessel(AT)brandeis.edu), Sep 03 2004
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