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A007113
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Expansion of (1 + x)^x.
(Formerly M0919)
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6
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1, 0, 2, -3, 20, -90, 594, -4200, 34544, -316008, 3207240, -35699400, 432690312, -5672581200, 79991160144, -1207367605080, 19423062612480, -331770360922560, 5997105160795584, -114373526841360000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 75
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FORMULA
| a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*k!*Stirling1(n-k, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 19 2004
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MATHEMATICA
| CoefficientList[Series[(1 + x)^x, {x, 0, 19}], x]*Table[(n - 1)!, {n, 1, 20}]
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CROSSREFS
| Cf. A053489, A053490. Apart from initial terms and signs, same as A066166.
Sequence in context: A151370 A041567 A087301 * A066166 A052804 A125763
Adjacent sequences: A007110 A007111 A007112 * A007114 A007115 A007116
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KEYWORD
| sign
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Signs from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998
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