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Search: id:A092923
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| A092923 |
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Number of permutations containing exactly one occurrence of the pattern #, with # one of {1-23, 3-21, 12-3, 32-1}. |
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+0
1
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| 1, 7, 39, 211, 1168, 6728, 40561, 256297, 1696707, 11752973, 85047284, 641782220, 5041634549, 41160207335, 348664792199, 3059885806071, 27781291314396, 260599397789924, 2522492941426381
(list; graph; listen)
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OFFSET
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3,2
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LINKS
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A. Claesson and T. Mansour, Counting patterns of type (1,2) or (2,1).
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FORMULA
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G.f.: sum{n>=1, x/(1-nx) * sum{k>=0, kx^(k+n)/prod[l=1..k+n, 1-lx]}}.
Recurrence: a(n) = 2a(n-1) + sum{k=0..n-3, C(n-2, k)*[a(k+1)+B(k+1)]}, with B(n) the Bell numbers A000110(n).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 2*a(n-1)+sum(k=0, n-3, binomial(n-2, k)*(a(k+1)+polcoeff(serlaplace(exp(exp(x)-1)), k+1))))
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CROSSREFS
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Sequence in context: A026708 A016127 A099460 this_sequence A125786 A071082 A122884
Adjacent sequences: A092920 A092921 A092922 this_sequence A092924 A092925 A092926
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Apr 18 2004
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