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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
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| Ira. M. Gessel, Generating functions and enumeration of sequences, Ph. D. Thesis, MIT, 1977.
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FORMULA
| E.g.f.= (sqrt(3)/2)exp(-x/2)/cos(sqrt(3)x/2 + Pi/6).
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EXAMPLE
| 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
| 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
| Sequence in context: A151277 A192368 A138748 * A054236 A118411 A091876
Adjacent sequences: A097896 A097897 A097898 * A097900 A097901 A097902
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ira Gessel (gessel(AT)brandeis.edu), Sep 03 2004
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