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%I #4 Mar 30 2012 18:37:05
%S 1,2,4,14,140,4964,808870,726210606,4161522164020,170403742275382924,
%T 54674613696351170731038,148019646825727958873435181692,
%U 3596203368022579371689526442266893534
%N a(0) = 1; for n>0, a(n) = number of binary partitions of the Catalan number A000108(n).
%H Alois P. Heinz, <a href="/A134040/b134040.txt">Table of n, a(n) for n = 0..30</a>
%F a(n) = A000123( A000108(n) ) for n>0 with a(0)=1, where A000108(n) = C(2*n,n)/(n+1) (Catalan numbers) and A000123(n) = number of partitions of 2n into powers of 2.
%e a(0)=1, a(1)=A000123(1)=2, a(2)=A000123(2)=4, a(3)=A000123(5)=14, a(4)=A000123(14)=140.
%Y Cf. A000123, A000108.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 02 2007
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