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A101851
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a(n) = Sum_{k=0..n} (-1)^(n-k)*k*Stirling2(n,k).
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1
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0, 1, 1, -2, -1, 11, -18, -41, 317, -680, -1767, 19911, -68264, -59643, 2076973, -11905466, 18577387, 269836343, -2819431570, 12357816867, 17355428041, -752675321800, 6318046208653, -21416130683133, -152569023028272, 3016508107668601, -23667435182395287
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| E.g.f.: (1-exp(-x))*exp(1-exp(-x)): G.f.: Sum(k*x^k/Product(1+l*x, l = 1 .. k), k = 1 .. infinity).
a(n) = Sum_{k=0..n} (-1)^(k+1)*binomial(n,k)*A000587(k+2) - Peter Luschny, Apr 17 2011
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MAPLE
| A101851 := proc(n) local k;
add((-1)^(n-k)*k*combinat[stirling2](n, k), k = 0..n) end:
seq(A101851(n), n = 0..26); # - Peter Luschny, Apr 17 2011
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CROSSREFS
| Cf. A005493, A000587.
Sequence in context: A138351 A120293 A063624 * A111724 A184299 A080371
Adjacent sequences: A101848 A101849 A101850 * A101852 A101853 A101854
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KEYWORD
| easy,sign
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 27 2005
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