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%I #31 Apr 08 2020 13:33:58
%S 0,0,0,0,0,0,0,0,0,1,11,67,299,1093,3473,9949,26333,65536,155382,
%T 354522,784626,1695222,3593934,7507638,15505590,31746651,64574877,
%U 130712029,263644133,530396371,1065084887,2136022699,4279934123,8570386546
%N a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,8).
%H Reinhard Zumkeller, <a href="/A035041/b035041.txt">Table of n, a(n) for n = 0..1000</a>
%H 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.
%H Ângela Mestre, José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
%F G.f.: x^9/((1-2*x)*(1-x)^9).
%p a:=n->sum(binomial(n,j),j=9..n): seq(a(n), n=0..33); # _Zerinvary Lajos_, Jan 04 2007
%t a=1;lst={};s1=s2=s3=s4=s5=s6=s7=s8=s9=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;s6+=s5;s7+=s6;s8+=s7;s9+=s8;AppendTo[lst,s9];a=a*2,{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009 *)
%t Table[Sum[ Binomial[n, k], {k, 9, n}], {n, 0, 33}] (* _Zerinvary Lajos_, Jul 08 2009 *)
%o (Haskell)
%o a035041 n = a035041_list !! n
%o a035041_list = map (sum . drop 9) a007318_tabl
%o -- _Reinhard Zumkeller_, Jun 20 2015
%Y a(n)= A055248(n, 9). Partial sums of A035040.
%Y Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.
%Y Cf. A007318.
%K nonn,easy
%O 0,11
%A _N. J. A. Sloane_
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