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A189924
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a(n) = abs(Stirling1(n+2,2)) - abs(Stirling1(n+2,3)).
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2
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1, 2, 5, 15, 49, 140, -64, -8540, -146124, -2124936, -30374136, -445116672, -6793958016, -108691150464, -1826654613120, -32257962443520, -598196854045440, -11635261535301120, -237044583523514880, -5050811716879104000
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OFFSET
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0,2
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COMMENTS
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This is the fourth (k=3) column sequence in triangle A094645 without leading zeros.
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LINKS
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FORMULA
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a(n) = abs(Stirling1(n+2,2)) - abs(Stirling1(n+2,3)), with the unsigned Stirling1 numbers abs(Stirling1(n,k)) = A132393(n,k).
E.g.f.: (1/2)*(2-log(1-x)^2)/(1-x)^2 (from differentiating three times (1-x)*((-log(1-x))^3)/3!).
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MATHEMATICA
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Table[Abs[StirlingS1[n+2, 2]]-Abs[StirlingS1[n+2, 3]], {n, 0, 20}] (* Harvey P. Dale, May 21 2015 *)
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PROG
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(Magma) [Abs(StirlingFirst(n+2, 2)) - Abs(StirlingFirst(n+2, 3)): n in [0..30]]; // G. C. Greubel, Jan 13 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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