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Search: id:A094646
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| A094646 |
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Generalized Stirling number triangle of first kind. |
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+0
4
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| 1, -2, 1, 2, -3, 1, 0, 2, -3, 1, 0, 2, -1, -2, 1, 0, 4, 0, -5, 0, 1, 0, 12, 4, -15, -5, 3, 1, 0, 48, 28, -56, -35, 7, 7, 1, 0, 240, 188, -252, -231, 0, 42, 12, 1, 0, 1440, 1368, -1324, -1638, -231, 252, 114, 18, 1, 0, 10080, 11016, -7900, -12790, -3255, 1533, 1050, 240, 25, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Triangle T(n,k), 0<=k<=n, read by rows, given by [ -2, 1, -1, 2, 0, 3, 1, 4, 2, 5, ...] DELTA [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 23 2006
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FORMULA
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E.g.f.: (1-y)^(2-x).
Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A000142(n), A000142(n+1), A001710(n+2), A001715(n+3), A001720(n+4), A001725(n+5), A001730(n+6), A049388(n), A049389(n), A049398(n), A051431(n) for x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 13 2007
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then |T(n,i)| =| f(n,i,-2)|, for n=1,2,...;i=0...n. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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EXAMPLE
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1 ; -2,1 ; 2,-3,1 ; 0,2,-3,1 ; 0,2,-1,-3,1 ; 0,4,0,-5,0,1 ; ...
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CROSSREFS
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Cf. A049444, A049458, A094645.
Sequence in context: A082501 A132815 A167684 this_sequence A124448 A143343 A138243
Adjacent sequences: A094643 A094644 A094645 this_sequence A094647 A094648 A094649
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), May 17 2004
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