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%I #17 Nov 30 2017 04:17:29
%S 5,25,155,1135,9545,90445,952175,11016595,138864365,1893369505,
%T 27756952355,435287980375,7269934161905,128812336516885,
%U 2413131201408695,47652865538001595,989254278781162325
%N Permanent of (0,1)-matrix of size n X (n+d) with d=4 and n-1 zeros not on a line.
%D Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.
%H Indranil Ghosh, <a href="/A090014/b090014.txt">Table of n, a(n) for n = 1..445</a>
%H Seok-Zun Song et al., <a href="http://dx.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+3)*a(n-1) + (n-2)*a(n-2), a(1)=5, a(2)=25.
%F a(n) ~ exp(-1) * n! * n^4 / 24. - _Vaclav Kotesovec_, Nov 30 2017
%t f[x_] := x*HypergeometricPFQ[{1, 5}, {}, x/(x+1)]/(x+1); Total /@ Partition[ CoefficientList[ Series[f[x], {x, 0, 18}], x], 2, 1] // Rest (* _Jean-François Alcover_, Nov 12 2013, after A001909 and _Mark van Hoeij_ *)
%t t={5,25};Do[AppendTo[t,(n+3)*t[[-1]]+(n-2)*t[[-2]]],{n,3,17}];t (* _Indranil Ghosh_, Feb 21 2017 *)
%Y a(n) = A001909(n-1) + A001909(n), a(1)=5
%Y Cf. A000255, A000153, A000261, A001909, A001910, A090010, A055790, A090012-A090016.
%K nonn,easy
%O 1,1
%A _Jaap Spies_, Dec 13 2003
%E Corrected by _Jaap Spies_, Jan 26 2004
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