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A006675
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Number of paths through an array.
(Formerly M2079)
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6
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0, 0, 2, 15, 104, 770, 6264, 56196, 554112, 5973264, 69998400, 886897440, 12089295360, 176484597120, 2748022986240, 45472329504000, 796983880089600, 14751208762214400, 287543058350284800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| A. M. Khidr and B. S. El-Desouky, A symmetric sum involving the Stirling numbers of the first kind, European J. Combin., 5 (1984), 51-54.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| a(n) = n*n! * (H[ n ] - 1), H[ n ] = sum[ k=1..n ] k^-1.
E.g.f. A(x) = x*(1-x)^-2 * (-log(1-x))
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EXAMPLE
| x*(1-x)^-2 * (-log(1-x)) = x^2 + 5/2*x^3 + 13/3*x^4 + 77/12*x^5 + ...
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MATHEMATICA
| a[n_] := n*n!*(HarmonicNumber[n]-1); Table[a[n], {n, 0, 18}] (* From Jean-François Alcover, Nov 28 2011 *)
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CROSSREFS
| Cf. A000254, A001705.
Sequence in context: A037641 A027080 A081018 * A037524 A037733 A037556
Adjacent sequences: A006672 A006673 A006674 * A006676 A006677 A006678
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Joe Keane (jgk(AT)jgk.org)
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