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%I #23 Jun 20 2015 09:34:09
%S 0,0,0,0,0,0,0,0,1,10,56,232,794,2380,6476,16384,39203,89846,199140,
%T 430104,910596,1898712,3913704,7997952,16241061,32828226,66137152,
%U 132932104,266752238,534688516,1070937812,2143911424,4290452423
%N a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,7).
%H Reinhard Zumkeller, <a href="/A035040/b035040.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.
%F G.f.: x^8/((1-2*x)*(1-x)^8).
%F 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 a:=n->sum(binomial(n,j),j=8..n): seq(a(n), n=0..32); # _Zerinvary Lajos_, Jan 04 2007
%t 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 *)
%o (Haskell)
%o a035040 n = a035040_list !! n
%o a035040_list = map (sum . drop 8) a007318_tabl
%o -- _Reinhard Zumkeller_, Jun 20 2015
%Y a(n)= A055248(n, 8). Partial sums of A035039.
%Y Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.
%Y Cf. A007318.
%K nonn,easy
%O 0,10
%A _N. J. A. Sloane_
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