Search: id:A008862
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%I A008862
%S A008862 1,2,4,8,16,32,64,128,256,512,1023,2036,4017,7814,14913,27824,50643,
%T A008862 89846,155382,262144,431910,695860,1097790,1698160,2579130,3850756,
%U A008862 5658537,8192524,11698223,16489546,22964087,31621024,43081973,58115146
%N A008862 Sum C(n,k), k=0..9.
%C A008862 a(n) is the number of compositions (ordered partitions) of n+1 into ten 
               or fewer parts [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 24 2009]
%D A008862 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
%F A008862 a(n) = sum( binomial( n+1, 2k-1 ) for k=1..5 ), compare A008860.
%F A008862 G.f.: (1-8x+29x^2-62x^3+86x^4-80x^5+50x^6-20x^7+5x^8)/(1-x)^10 a(n)= 
               (n^9-27n^8+366n^7-2646n^6+12873n^5-31563n^4+79064n^3+34236n^2+270576n+362880)/
               9! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 
               2009]
%e A008862 a(10)=1023 because there are (2^10)-1 compositions of 11 into ten or 
               fewer parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 24 2009]
%Y A008862 Cf. A008859, A008860, A008861, A008863, A006261, A000127.
%Y A008862 Sequence in context: A115213 A009714 A051535 this_sequence A145116 A122265 
               A113010
%Y A008862 Adjacent sequences: A008859 A008860 A008861 this_sequence A008863 A008864 
               A008865
%K A008862 nonn
%O A008862 0,2
%A A008862 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy

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