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Search: id:A086226
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| A086226 |
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Number of permutations of length n containing exactly one occurrence of the pattern 1-32. |
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+0
2
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| 0, 0, 1, 9, 73, 637, 6220, 68414, 844067, 11589987, 175612351, 2912695193, 52502754076, 1022091626496, 21372127906257, 477737240288353, 11368449905784189, 286935157928114989, 7656210527253978232
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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A. Claesson and T. Mansour, Counting Occurrences of a Pattern of Type (1,2) or (2,1) in Permutations, Advances in Applied Mathematics, 29 (2002), 293-310
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FORMULA
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a(0)=0; a(n)=a(n-1)+sum(k=1, n-1, binomial(n, k)*a(k)+binomial(n-1, k-1)*B(k))) where B(k) is the k-th Bell number.
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PROGRAM
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(PARI) B(n)=round(exp(-1)*sum(k=0, 200, k^n/k!)); //an=vector(100); a(n)=if(n<1, 0, an[n]); //for(n=1, 30, an[n]=a(n-1)+sum(k=1, n-1, binomial(n, k)*a(k)+binomial(n-1, k-1)*B(k)))
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CROSSREFS
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Sequence in context: A023001 A015454 A121246 this_sequence A015465 A075232 A037533
Adjacent sequences: A086223 A086224 A086225 this_sequence A086227 A086228 A086229
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 28 2003
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