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Search: id:A081048
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| A081048 |
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Signed Stirling numbers of the first kind. |
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+0
3
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| 0, 1, -3, 11, -50, 274, -1764, 13068, -109584, 1026576, -10628640, 120543840, -1486442880, 19802759040, -283465647360, 4339163001600, -70734282393600, 1223405590579200, -22376988058521600, 431565146817638400, -8752948036761600000, 186244810780170240000
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n)=n!*Sum {k=1..n, (-1)^(n+1)*1/k} E.g.f. (1+x)^-1 * log(1+x).
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EXAMPLE
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a(9): coefficient of p^2 in polynomial p (p - 1) (p - 2) (p - 3) (p - 4) (p - 5) (p - 6) (p - 7) (p - 8) = -1 + 40320 p - 109584 p^2 + 118124 p^3 - 67284 p^4 + 22449 p^5 - 4536 p^6 + 546 p^7 - 36 p^8 + p^9 is equal to -109584. [From Artur Jasinski (grafix(AT)csl.pl), Nov 30 2008]
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MATHEMATICA
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aa = {}; Do[AppendTo[aa, Coefficient[Expand[Product[p - n, {n, 0, m}]], p, 2]], {m, 1, 20}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 30 2008]
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CROSSREFS
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Cf. A000254, A008275.
Sequence in context: A115081 A103466 A000254 this_sequence A065048 A024335 A024336
Adjacent sequences: A081045 A081046 A081047 this_sequence A081049 A081050 A081051
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 05 2003
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