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A000276
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Associated Stirling numbers.
(Formerly M3075 N1248)
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7
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3, 20, 130, 924, 7308, 64224, 623376, 6636960, 76998240, 967524480, 13096736640, 190060335360, 2944310342400, 48503818137600, 846795372595200, 15618926924697600, 303517672703078400, 6198400928176128000, 132720966600284160000, 2973385109386137600000
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OFFSET
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4,1
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COMMENTS
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a(n) is also the number of permutations of n elements, without any fixed point, with exactly two cycles. - Shanzhen Gao, Sep 15 2010
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REFERENCES
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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).
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LINKS
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FORMULA
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a(n) = (n-1)!*Sum_{i=2..n-2} 1/i = (n-1)!*(Psi(n-1)+gamma-1). - Vladeta Jovovic, Aug 19 2003
With alternating signs: Ramanujan polynomials psi_3(n-2, x) evaluated at 1. - Ralf Stephan, Apr 16 2004
a(n) = Sum_{i=2..floor((n-1)/2)} n!/((n-i)*i) + Sum_{i=ceiling(n/2)..floor(n/2)} n!/(2*(n-i)*i). - Shanzhen Gao, Sep 15 2010
a(n) = (n+3)!*(h(n+2)-1), with offset 0, where h(n)=sum(1/k,k=1..n). - Gary Detlefs, Sep 11 2010
Conjecture: (-n+2)*a(n) +(n-1)*(2*n-5)*a(n-1) -(n-1)*(n-2)*(n-3)*a(n-2)=0. - R. J. Mathar, Jul 18 2015
Conjecture: a(n) +2*(-n+2)*a(n-1) +(n^2-6*n+10)*a(n-2) +(n-3)*(n-4)*a(n-3)=0. - R. J. Mathar, Jul 18 2015
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EXAMPLE
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a(4) = 3 because we have: (12)(34),(13)(24),(14)(23). - Geoffrey Critzer, Nov 03 2012
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MATHEMATICA
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nn=25; a=Log[1/(1-x)]-x; Drop[Range[0, nn]!CoefficientList[Series[a^2/2, {x, 0, nn}], x], 4] (* Geoffrey Critzer, Nov 03 2012 *)
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PROG
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(PARI) a(n) = (n-1)!*sum(i=2, n-2, 1/i); \\ Michel Marcus, Feb 06 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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