A006675 Number of paths through an array. (Formerly M2079)

0, 0, 2, 15, 104, 770, 6264, 56196, 554112, 5973264, 69998400, 886897440, 12089295360, 176484597120, 2748022986240, 45472329504000, 796983880089600, 14751208762214400, 287543058350284800

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) where H(n) = Sum_{k=1..n} 1/k.

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-François Alcover, Nov 28 2011 *)

Crossrefs

Cf. A000254, A001705.

Sequence in context: A293045 A372264 A081018 * A215643 A332048 A295268

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