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%I #34 Sep 08 2022 08:45:01
%S 1,5,16,42,98,210,420,792,1419,2431,4004,6370,9828,14756,21624,31008,
%T 43605,60249,81928,109802,145222,189750,245180,313560,397215,498771,
%U 621180,767746,942152,1148488,1391280,1675520,2006697,2390829,2834496,3344874,3929770
%N T(2n+3,n), array T as in A055794.
%C If Y is a 2-subset of an n-set X then, for n>=6, a(n-6) is the number of 6-subsets of X which do not have exactly one element in common with Y. - _Milan Janjic_, Dec 28 2007
%H Vincenzo Librandi, <a href="/A055796/b055796.txt">Table of n, a(n) for n = 0..1000</a>
%H Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (n+1)(n+2)(n+3)(n+4)(n^2-n+30)/720.
%F a(n-4) = binomial(n,6) + binomial(n,4) for n>3. - _Zerinvary Lajos_, Jul 24 2006
%F G.f.: (1-2*x+2*x^2)/(1-x)^7. - _Colin Barker_, Feb 22 2012
%p seq(binomial(n+4, 6)+binomial(n+4, 4), n=0..33) # _Zerinvary Lajos_, Jul 24 2006
%t a=1;b=2;c=3;d=4;s=5;lst={1,s};Do[a+=n;b+=a;c+=b;d+=c;s+=d;AppendTo[lst,s],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 24 2009 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,5,16,42,98, 210,420},50] (* _Vincenzo Librandi_, Apr 30 2012 *)
%t Table[(n+1)(n+2)(n+3)(n+4)(n^2-n+30)/720,{n,0,50}] (* _Harvey P. Dale_, Feb 12 2013 *)
%o (Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+30)/720: n in [0..40]]; // _Vincenzo Librandi_, Apr 30 2012
%Y Cf. A051601.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 28 2000
%E More terms from _Harvey P. Dale_, Feb 12 2013
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