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A086226 Number of permutations of length n containing exactly one occurrence of the pattern 1-32. 0
0, 0, 1, 9, 73, 637, 6220, 68414, 844067, 11589987, 175612351, 2912695193, 52502754076, 1022091626496, 21372127906257, 477737240288353, 11368449905784189, 286935157928114989, 7656210527253978232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

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

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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.

PROG

(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)))

CROSSREFS

Sequence in context: A277672 A015454 A121246 * A199677 A197676 A197534

Adjacent sequences:  A086223 A086224 A086225 * A086227 A086228 A086229

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Aug 28 2003

STATUS

approved

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Last modified March 24 19:55 EDT 2017. Contains 283991 sequences.