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%I #10 Feb 26 2018 20:46:49
%S 1,1,1,1,2,1,1,3,2,0,1,4,4,1,0,1,5,6,2,0,0,1,6,9,4,0,0,0,1,7,12,6,0,0,
%T 0,0,1,8,16,10,1,0,0,0,0,1,9,20,14,2,0,0,0,0,0,1,10,25,20,4,0,0,0,0,0,
%U 0,1,11,30,26,6,0,0,0,0,0,0,0,1,12,36,35,10,0,0,0,0,0,0,0,0,1,13,42,44
%N Triangle of number of partitions of 2n into powers of 2 where the largest part is 2^k.
%C In the recurrence T(n,k)=T(n-1,k)+T([n/2],k-1): T(n-1,k) represents the partitions where the smallest part is 1 and T([n/2],k-1) those where it is not.
%H H. Bottomley, <a href="/A000123/a000123.gif">Illustration of initial terms</a>
%F T(n, k) = T(n-1, k)+T([n/2], k-1) starting with T(n, 0)=1 and T(0, k)=0 for k>0.
%e Rows start:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 2, 0;
%e 1, 4, 4, 1, 0;
%e 1, 5, 6, 2, 0, 0;
%e ...
%Y Columns include A000012, A000027, A002620, A008804. Subsequent columns start like A000123 (offset). Row sums are A000123.
%K easy,nonn,tabl
%O 0,5
%A _Henry Bottomley_, Aug 02 2002
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