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A229002
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Total sum of the n-th powers of lengths of ascending runs in all permutations of [n].
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2
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0, 1, 6, 66, 1110, 25620, 765506, 28544040, 1293790126, 69860663220, 4422094936842, 323816329558128, 27127369640967206, 2575241880204602700, 274755427187762475922, 32708158728316937527944, 4316964980670466411606110, 628131523035069583394938980
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k^n * A122843(n,k).
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MAPLE
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a:= n-> add(`if`(n=k, 1, n!/(k+1)!*(k*(n-k+1)+1
-((k+1)*(n-k)+1)/(k+2)))*k^n, k=1..n):
seq(a(n), n=1..20);
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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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