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A000276
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Associated Stirling numbers.
(Formerly M3075 N1248)
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5
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3, 20, 130, 924, 7308, 64224, 623376, 6636960, 76998240, 967524480, 13096736640, 190060335360, 2944310342400, 48503818137600, 846795372595200, 15618926924697600, 303517672703078400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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COMMENTS
| a(n) is also the number of permutations of n elements, without any fixed point, with exactly two cycles. [From Shanzhen Gao (shanzhengao(AT)yahoo.com), Sep 15 2010]
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 75.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Shanzhen Gao, Permutations with Restricted Structure (in preparation) [From Shanzhen Gao (shanzhengao(AT)yahoo.com), Sep 15 2010]
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FORMULA
| a(n) = (n-1)!*Sum _{i=2..n-2} 1/i = (n-1)!*(Psi(n-1)+gamma-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2003
With alternating signs: Ramanujan polynomials psi_3(n-2, x) evaluated at 1. - Ralf Stephan, Apr 16 2004
E.g.f. ((x+ln(1-x))^2)/2. [Corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), May 03 2008]
$\dsum\limits_{i=2}^{\lfloor (n-1)/2\rfloor }\frac{n!}{(n-i)i}% +\dsum\limits_{i=\lceil n/2\rceil }^{\lfloor n/2\rfloor }\frac{n!}{2(n-i)i}$ [From Shanzhen Gao (shanzhengao(AT)yahoo.com), Sep 15 2010]
a(n)=(n+3)!*(h(n+2)-1), with offset 0, where h(n)=sum(1/k,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Sep 11 2010]
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CROSSREFS
| A diagonal of triangle in A008306.
Cf. A052518, A052881.
Sequence in context: A187442 A167590 A138910 * A056306 A056298 A114479
Adjacent sequences: A000273 A000274 A000275 * A000277 A000278 A000279
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net).
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