A006675 Number of paths through an array.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

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

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.

Crossrefs

Cf. A000254, A001705.

Programs

Mathematica

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

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

Extensions

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