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Search: id:A097899
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| A097899 |
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Number of permutations of [n] with no runs of length 1. (The permutation 3574162 has two runs of length 1: 357/4/16/2). |
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+0
1
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| 1, 0, 1, 1, 6, 19, 109, 588, 4033, 29485, 246042, 2228203, 22162249, 237997032, 2757055393, 34191395785, 452480427678, 6360924613699, 94691284984405, 1487846074481172, 24608991911033377, 427379047337272213
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OFFSET
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0,5
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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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E.g.f.= (sqrt(3)/2)exp(-x/2)/cos(sqrt(3)x/2 + Pi/6).
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EXAMPLE
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Example: a(4)=6 because 1234, 1324, 1423, 2314, 2413, 3412 are the only permutations of [4] with no runs of length 1.
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MAPLE
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G:=sqrt(3)*exp(-x/2)/2/cos(sqrt(3)*x/2+Pi/6): Gser:=series(G, x=0, 26): 1, seq(n!*coeff(Gser, x^n), n=1..25);
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CROSSREFS
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Adjacent sequences: A097896 A097897 A097898 this_sequence A097900 A097901 A097902
Sequence in context: A041937 A111510 A138748 this_sequence A054236 A118411 A091876
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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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