This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096943 #9 Jul 31 2015 12:59:05 %S A096943 5,26,81,196,406,756,1302,2112,3267,4862,7007,9828,13468,18088,23868, %T A096943 31008,39729,50274,62909,77924,95634,116380,140530,168480,200655, %U A096943 237510,279531,327236,381176,441936,510136,586432,671517,766122,871017,987012 %N A096943 Sixth column of (1,5)-Pascal triangle A096940. %C A096943 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 A096943 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1). %F A096943 G.f.: (5-4*x)/(1-x)^6. %F A096943 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 A096943 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 A096943 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 A096943 Fifth column: A096942; seventh column: A096944. %K A096943 nonn,easy %O A096943 0,1 %A A096943 _Wolfdieter Lang_, Jul 16 2004