%I A008863
%S A008863 1,2,4,8,16,32,64,128,256,512,1024,2047,4083,8100,15914,30827,58651,
%T A008863 109294,199140,354522,616666,1048576,1744436,2842226,4540386,7119516,
%U A008863 10970272,16628809,24821333,36519556,53009102,75973189,107594213
%N A008863 Sum C(n,k), k=0..10.
%C A008863 a(n) is the number of compositions (ordered partitions) of n+1 into eleven 
               or fewer parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 24 2009]
%D A008863 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
%F A008863 a(n)=sum(binomial(n+1, 2k), k=0..5), compare A008859.
%F A008863 G.f.:(1-9x+37x^2-91x^3+148x^4-166x^5+130x^6-70x^7+25x^8-5x^9+x^10)/(1-x)^11 
               a(n)= (n^10-35n^9+600n^8-5790n^7+36813n^6-140595n^5+408050n^4-382060n^3+1368936n^2+2342880n+3628800)/
               10! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 
               24 2009]
%e A008863 a(11)=2047 because there are 2^11=2048 compositions of 12 into any size 
               parts but one of the compositions (1+1+...+1=12) has more than eleven 
               parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 
               24 2009]
%Y A008863 Cf. A008859, A008860, A008861, A008862, A006261, A000127.
%Y A008863 Sequence in context: A122265 A113010 A056767 this_sequence A145117 A133025 
               A118655
%Y A008863 Adjacent sequences: A008860 A008861 A008862 this_sequence A008864 A008865 
               A008866
%K A008863 nonn
%O A008863 0,2
%A A008863 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy