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 A120478 #16 Sep 01 2025 17:36:15
%S A120478 6,21,56,126,252,461,786,1266,1946,2877,4116,5726,7776,10341,13502,
%T A120478 17346,21966,27461,33936,41502,50276,60381,71946,85106,100002,116781,
%U A120478 135596,156606,179976,205877,234486,265986,300566,338421,379752,424766
%N A120478 a(n) = binomial(n+6,5) - binomial(n,5).
%H A120478 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A120478 a(n) = A008488(n+1). - _R. J. Mathar_, Aug 07 2008
%F A120478 From _Harvey P. Dale_, May 04 2011: (Start)
%F A120478 a(0)=6, a(1)=21, a(2)=56, a(3)=126, a(4)=252, a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
%F A120478 G.f.: (-6 + 9*x - 11*x^2 + 4*x^3 - 2*x^4)/(-1 + x)^5. (End)
%p A120478 [seq(binomial(n+6,5)-binomial(n,5),n=0..45)];
%t A120478 Table[Binomial[n+6,5]-Binomial[n,5],{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{6,21,56,126,252},40] (* _Harvey P. Dale_, May 04 2011 *)
%K A120478 easy,nonn,changed
%O A120478 0,1
%A A120478 _Zerinvary Lajos_, Jul 21 2006