A090010 - OEIS

%I #22 Jul 01 2022 05:34:07

%S 6,43,356,3333,34754,398959,4996032,67741129,988344062,15434831091,

%T 256840738076,4536075689293,84731451264186,1668866557980343,

%U 34563571477305464,750867999393119889,17072113130285524982,405423357986250112699,10037458628015142154452

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

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

%H Vincenzo Librandi, <a href="/A090010/b090010.txt">Table of n, a(n) for n = 1..200</a>

%H Seok-Zun Song et al., <a href="https://doi.org/10.1016/S0024-3795(03)00382-3">Extremes of permanents of (0,1)-matrices</a>, Lin. Algebra and its Applic. 373 (2003), pp. 197-210.

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

%F G.f.: -1+hypergeom([1,7],[],x/(x+1))/(x+1) - _Mark van Hoeij_, Nov 07 2011

%F E.g.f.: -1 + exp(-x)/(1-x)^7. - _Vaclav Kotesovec_, Oct 21 2012

%F a(n) ~ n!*n^6/(720*e). - _Vaclav Kotesovec_, Oct 21 2012

%p 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);

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

%o (PARI) x='x+O('x^66); Vec(serlaplace(-1+exp(-x)/(1-x)^7)) \\ _Joerg Arndt_, May 11 2013

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

%K nonn,easy

%O 1,1

%A _Jaap Spies_, Dec 13 2003

%E Corrected by _Jaap Spies_, Jan 26 2004