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A092603
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a(n) = sum [k = 1 to n] min{k!, binom(n,k)}.
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1
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1, 2, 4, 8, 15, 31, 62, 126, 283, 539, 1177, 2459, 4969, 10781, 22297, 45116, 95759, 201615, 400755, 830859, 1741455, 3505627, 7099561, 14607199, 30112789, 60176505, 121626832, 247652036, 504389269, 1010060135, 2030792857
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Upper bound on A088532[n].
The number of patterns of length k in a permutation of length n is bounded above by k! and binom(n,k). The total number of patterns in a permutation of length n is therefore bounded above by the sum of the smaller of these two upper bounds.
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MATHEMATICA
| Table[Sum[Min[k!, Binomial[n, k]], {k, 1, n}], {n, 1, 40}]
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CROSSREFS
| Cf. A088532.
Sequence in context: A068030 A191497 A052325 * A086125 A061030 A036661
Adjacent sequences: A092600 A092601 A092602 * A092604 A092605 A092606
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KEYWORD
| easy,nonn
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AUTHOR
| Rob Pratt (Rob.Pratt(AT)sas.com), Apr 10 2004
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