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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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1
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0, 0, 1, 9, 73, 637, 6220, 68414, 844067, 11589987, 175612351, 2912695193, 52502754076, 1022091626496, 21372127906257, 477737240288353, 11368449905784189, 286935157928114989, 7656210527253978232
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OFFSET
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0,4
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LINKS
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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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MATHEMATICA
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PROG
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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)));
an
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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