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A088436
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Number of permutations in the symmetric group S_n that have exactly one transposition in their cycle decomposition.
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2
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0, 1, 3, 6, 30, 225, 1575, 12180, 109620, 1100925, 12110175, 145259730, 1888376490, 26438216805, 396573252075, 6345155817000, 107867648889000, 1941617990136825, 36890741812599675, 737814829704702750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 189, Exercise 19 for k=1. With (-1)^k omitted.
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FORMULA
| a(n)=n!*sum(((-1)^j)/(j!*2^j),j=0..floor(n/2)-k)/(k!*2^k), n>=1.
E.g.f.: x^2/(1-x)/2*exp(-x^2/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 09 2003
Contribution from Weisenhorn Paul (weisenhorn-f.p(AT)online.de), Jun 02 2010: In general, for k cycles of length 2, a(n)=n!*sum((-1)^j/((j-k)!*2^j*k!),j=k..n div 2), g.f. = (exp(-z^2/2)*z^2*k)/((1-z)*2^k*k!)
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MAPLE
| Contribution from Weisenhorn Paul (weisenhorn-f.p(AT)online.de), Jun 02 2010: (Start)
G=(exp(-z^2/2)*z^2*k)/((1-z)*2^k*k!): Gser=series(G, z=0, 21):
for n from 2*k to 20 do a(n)=n!*coeff(Gser, z, n): end do:
(End)
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MATHEMATICA
| d=Exp[-x^2/2]/(1-x); Range[0, 20]! CoefficientList[Series[(x^2/2! )d, {x, 0, 20}], x] (* Geoffrey Critzer, Nov 29 2011 *)
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CROSSREFS
| Cf. A000266, A027616, A000240.
Sequence in context: A090932 A157534 A133799 * A088506 A061137 A012280
Adjacent sequences: A088433 A088434 A088435 * A088437 A088438 A088439
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KEYWORD
| nonn
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AUTHOR
| Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
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EXTENSIONS
| More terms from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 22 2008
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