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A051684
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Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 2.
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2
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0, -1, -3, -3, 5, 15, -21, -133, 27, 1215, 935, -12441, -23673, 138047, 469455, -1601265, -9112561, 18108927, 182135007, -161934625, -3804634785, -404007681, 83297957567
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.
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FORMULA
| a(n) = c(n, 2), where c(n, d)=Sum_{k=1..n} (-1)^(k+1)*(n-1)!/(n-k)! *Sum_{l:lcm{k, l}=d} c(n-k, l), c(0, 1)=1.
a(n)=2*A048099(n)-A001189(n)=A048099(n)-A001465(n) a(n)=(-1)^n*A001464(n)-1 a(n)=a(n-1)-(n-1)*(a(n-2)+1) E.g.f.: -e^x+e^(x-(1/2)*x^2) - Matthew J. White (mattjameswhite(AT)hotmail.com), Mar 02 2006
a(n) = Sum((-1)^j*n!/(2^j*j!*(n-2*j)!),j=1..floor(n/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 06 2006
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CROSSREFS
| Cf. A001189, A051685.
Sequence in context: A095355 A069834 A064038 * A195583 A139431 A144423
Adjacent sequences: A051681 A051682 A051683 * A051685 A051686 A051687
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KEYWORD
| sign
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs)
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