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A084417
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Triangle read by rows: T(n,k)=sum((n+1-i)!*stirling2(n,n+1-i),i=1..k), n>=1, 1<=k<=n.
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1
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1, 2, 3, 6, 12, 13, 24, 60, 74, 75, 120, 360, 510, 540, 541, 720, 2520, 4080, 4620, 4682, 4683, 5040, 20160, 36960, 45360, 47166, 47292, 47293, 40320, 181440, 372960, 498960, 539784, 545580, 545834, 545835, 362880, 1814400, 4142880, 6048000
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OFFSET
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1,2
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COMMENTS
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Interpolates between A000670 and factorials.
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LINKS
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FORMULA
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T(n, k)=sum((n+1-i)!*stirling2(n, n+1-i), i=1..k), n>=1, 1<=k<=n.
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EXAMPLE
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1;2,3;6,12,13;24,60,74,75;120,360,510,540,541;
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MAPLE
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with(combinat): T:=(n, k)->sum((n+1-i)!*stirling2(n, n+1-i), i=1..k): seq(seq(T(n, k), k=1..n), n=1..10);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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