A090010 Permanent of (0,1)-matrix of size n X (n+d) with d=6 and n zeros not on a line.

6, 43, 356, 3333, 34754, 398959, 4996032, 67741129, 988344062, 15434831091, 256840738076, 4536075689293, 84731451264186, 1668866557980343, 34563571477305464, 750867999393119889, 17072113130285524982, 405423357986250112699, 10037458628015142154452

Offset: 1

Author

Jaap Spies, Dec 13 2003

Keywords

• nonn
• easy

References

• Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), pp. 197-210.

Crossrefs

Cf. A000255, A000153, A000261, A001909, A001910, A055790, A090012-A090016.

Programs

Maple

A090010 := proc(n,d) local r; if (n=1) then r := d elif (n=2) then r := d^2+d+1 else r := (n+d-1)*A090010(n-1,d)+(n-1)*A090010(n-2,d) fi; RETURN(r); end: seq(A090010(n,6),n=1..18);

Mathematica

Rest[CoefficientList[Series[E^(-x)/(1-x)^7,{x,0,20}],x]*Range[0,20]!] (* Vaclav Kotesovec, Oct 21 2012 *)

PARI

x='x+O('x^66); Vec(serlaplace(-1+exp(-x)/(1-x)^7)) \\ Joerg Arndt, May 11 2013

Formula

a(n) = (n+5)*a(n-1) + (n-1)*a(n-2), a(1)=6, a(2)=43

G.f.: -1+hypergeom([1,7],[],x/(x+1))/(x+1) - Mark van Hoeij, Nov 07 2011

E.g.f.: -1 + exp(-x)/(1-x)^7. - Vaclav Kotesovec, Oct 21 2012

a(n) ~ n!*n^6/(720*e). - Vaclav Kotesovec, Oct 21 2012

Extensions

Corrected by Jaap Spies, Jan 26 2004