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 A032774 #20 Dec 08 2021 09:49:40
%S A032774 0,180,1152,4320,12342,29700,63360,123552,224640,386100,633600,
%T A032774 1000182,1527552,2267460,3283200,4651200,6462720,8825652,11866422,
%U A032774 15732000,20592000,26640900,34100352,43221600,54288000,67617642,83566080,102529152,124945920,151301700,182131200
%N A032774 a(n) = floor( n*(n+1)*(n+2)*...*(n+6) / (n+(n+1)+(n+2)+...+(n+6)) ).
%C A032774 In general, such sequences a(n) = floor((Product_{m=0..k} n+i) / (Sum_{m=0..k} n+i)) have rational generating functions. - _Georg Fischer_, Feb 23 2021
%H A032774 Harvey P. Dale, <a href="/A032774/b032774.txt">Table of n, a(n) for n = 0..1000</a>
%H A032774 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).
%p A032774 seq(coeff(series( -(6*x^10-36*x^9 + 90*x^8 - 120*x^7 - 90*x^6 - 108*x^5 - 102*x^4 - 108*x^3 - 72*x^2 - 180*x) / (-x^13+6*x^12 - 15*x^11+20*x^10 - 15*x^9+6*x^8 - x^7+x^6 - 6*x^5+15*x^4 - 20*x^3+15*x^2 - 6*x + 1) , x, n+1), x, n), n = 0..40); # _Georg Fischer_, Feb 23 2021
%t A032774 Table[Floor[(Times @@ Range[n, n + 6])/(7 n + 21)], {n, 0, 30}] (* _Harvey P. Dale_, May 16 2020 *)
%Y A032774 Cf. A032775, A032776.
%Y A032774 Cf. A004526 (k=2), A032765 (k=3), A032768 (k=4), A032771 (k=5), A032774 (k=6), A032777 (k=7), A032780 (k=8), A032790 (k=9).
%K A032774 nonn,easy
%O A032774 0,2
%A A032774 _Patrick De Geest_, May 15 1998
%E A032774 More terms from _Georg Fischer_, Feb 23 2021