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 A063417 #22 Jun 13 2015 00:50:29
%S A063417 5,36,149,470,1251,2954,6371,12789,24210,43637,75438,125801,203294,
%T A063417 319545,490058,735182,1081251,1561914,2219675,3107664,4291661,5852396,
%U A063417 7888149,10517675,13883480,18155475,23535036
%N A063417 Ninth column (k=8) of septinomial array A063265.
%H A063417 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F A063417 a(n) = A063265(n+2,8) = (n+1)*(n+2)*(n^6 +41*n^5 +701*n^4 +6439*n^3 +33930*n^2 +100008*n +100800)/8!.
%F A063417 G.f.: (5-9*x+5*x^2+5*x^3-9*x^4+5*x^5-x^6)/(1-x)^9; the numerator polynomial is N6(8,x) from row n=8 of array A063266.
%F A063417 a(n) = 5*C(n+2,2) + 21*C(n+2,3) + 35*C(n+2,4) + 35*C(n+2,5) + 21*C(n+2,6) + 7*C(n+2,7) + C(n+2,8) (see comment in A213889). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012
%F A063417 a(0)=5, a(1)=36, a(2)=149, a(3)=470, a(4)=1251, a(5)=2954, a(6)=6371, a(7)=12789, a(8)=24210, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - _Harvey P. Dale_, Aug 22 2012
%t A063417 Table[Total[Table[Binomial[n+2,i],{i,2,8}]{5,21,35,35,21,7,1}],{n,0,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{5,36,149,470,1251,2954,6371,12789,24210},30] (* _Harvey P. Dale_, Aug 22 2012 *)
%Y A063417 Cf. A063267.
%K A063417 nonn,easy
%O A063417 0,1
%A A063417 _Wolfdieter Lang_, Jul 24 2001