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 A035040 #25 Aug 27 2025 15:56:45
%S A035040 0,0,0,0,0,0,0,0,1,10,56,232,794,2380,6476,16384,39203,89846,199140,
%T A035040 430104,910596,1898712,3913704,7997952,16241061,32828226,66137152,
%U A035040 132932104,266752238,534688516,1070937812,2143911424,4290452423
%N A035040 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,7).
%H A035040 Reinhard Zumkeller, <a href="/A035040/b035040.txt">Table of n, a(n) for n = 0..1000</a>
%H A035040 J. Eckhoff, <a href="http://dx.doi.org/10.1007/BF01297698">Der Satz von Radon in konvexen Produktstrukturen II</a>, Monat. f. Math., 73 (1969), 7-30.
%F A035040 G.f.: x^8/((1-2*x)*(1-x)^8).
%F A035040 a(n) = sum_{k=0..n} C(n, k+8) = sum_{k=8..n} C(n, k); a(n) = 2a(n-1) + C(n-1, 7). - _Paul Barry_, Aug 23 2004
%p A035040 a:=n->sum(binomial(n,j),j=8..n): seq(a(n), n=0..32); # _Zerinvary Lajos_, Jan 04 2007
%t A035040 a=1;lst={};s1=s2=s3=s4=s5=s6=s7=s8=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;s6+=s5;s7+=s6;s8+=s7;AppendTo[lst,s8];a=a*2,{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009 *)
%t A035040 Table[2^n-Total[Binomial[n,Range[0,7]]],{n,0,40}] (* _Harvey P. Dale_, Aug 27 2025 *)
%o A035040 (Haskell)
%o A035040 a035040 n = a035040_list !! n
%o A035040 a035040_list = map (sum . drop 8) a007318_tabl
%o A035040 -- _Reinhard Zumkeller_, Jun 20 2015
%Y A035040 a(n)= A055248(n, 8). Partial sums of A035039.
%Y A035040 Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.
%Y A035040 Cf. A007318.
%K A035040 nonn,easy,changed
%O A035040 0,10
%A A035040 _N. J. A. Sloane_