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Search: id:A105794
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| A105794 |
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Inverse of a generalized Stirling number triangle of first kind. |
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+0
4
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| 1, -1, 1, 1, -1, 1, -1, 1, 0, 1, 1, -1, 1, 2, 1, -1, 1, 0, 5, 5, 1, 1, -1, 1, 10, 20, 9, 1, -1, 1, 0, 21, 70, 56, 14, 1, 1, -1, 1, 42, 231, 294, 126, 20, 1, -1, 1, 0, 85, 735, 1407, 924, 246, 27, 1, 1, -1, 1, 170, 2290, 6363, 6027, 2400, 435, 35, 1
(list; table; graph; listen)
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OFFSET
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0,14
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COMMENT
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Inverse of number triangle A105793. Row sums are the generalized Bell numbers A000296.
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FORMULA
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Term k in row n is given by {(-1)^(k+n) * [sum from j=0 to j=k of (-1)^j * binomial(k,j) * (1-j)^n] / k! }; i.e. a finite difference. - Tom Copeland (tcjpn(AT)msn.com), Jun 05 2006
O.G.F. for row n = n-th finite difference of the Touchard (Bell) polynomials, T(x,j) and so the E.G.F. for these finite differences and therefore the sequence = exp{x*[exp(t)-1]-t} = exp{t*[T(x,.)-1]} umbrally. - Tom Copeland (tcjpn(AT)msn.com), Jun 05 2006
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CROSSREFS
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Sequence in context: A153462 A126310 A109086 this_sequence A160380 A122433 A056977
Adjacent sequences: A105791 A105792 A105793 this_sequence A105795 A105796 A105797
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 20 2005
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