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%I #9 Jul 31 2015 12:59:05
%S 5,26,81,196,406,756,1302,2112,3267,4862,7007,9828,13468,18088,23868,
%T 31008,39729,50274,62909,77924,95634,116380,140530,168480,200655,
%U 237510,279531,327236,381176,441936,510136,586432,671517,766122,871017,987012
%N Sixth column of (1,5)-Pascal triangle A096940.
%C If Y is a 5-subset of an n-set X then, for n>=9, a(n-9) is the number of 5-subsets of X having at most one element in common with Y. - _Milan Janjic_, Dec 08 2007
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F G.f.: (5-4*x)/(1-x)^6.
%F a(n)= (n+25)*binomial(n+4, 4)/5 = 5*b(n)-4*b(n-1), with b(n):= A000389(n+5)=binomial(n+5, 5).
%F a(0)=5, a(1)=26, a(2)=81, a(3)=196, a(4)=406, a(5)=756, a(n)=6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - _Harvey P. Dale_, Jan 11 2014
%t CoefficientList[Series[(5-4x)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{5,26,81,196,406,756},40] (* _Harvey P. Dale_, Jan 11 2014 *)
%Y Fifth column: A096942; seventh column: A096944.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jul 16 2004
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