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A006675 Number of paths through an array.
(Formerly M2079)
8
0, 0, 2, 15, 104, 770, 6264, 56196, 554112, 5973264, 69998400, 886897440, 12089295360, 176484597120, 2748022986240, 45472329504000, 796983880089600, 14751208762214400, 287543058350284800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=0..100

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.

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)).

a(n) = A001705(n) - A000254(n). - Peter Bala, Feb 12 2019

EXAMPLE

x*(1-x)^-2 * (-log(1-x)) = x^2 + 5/2*x^3 + 13/3*x^4 + 77/12*x^5 + ...

MATHEMATICA

a[n_] := n*n!*(HarmonicNumber[n]-1); Table[a[n], {n, 0, 18}] (* Jean-Fran├žois Alcover, Nov 28 2011 *)

CROSSREFS

Cf. A000254, A001705.

Sequence in context: A208347 A293045 A081018 * A215643 A295268 A037524

Adjacent sequences:  A006672 A006673 A006674 * A006676 A006677 A006678

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)