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%I #4 May 10 2013 12:44:59
%S 1,1,1,1,1,1,1,1,1,2,1,1,2,2,1,1,1,2,3,1,2,1,1,2,3,3,2,2,1,1,2,4,3,4,
%T 2,2,1,1,2,4,4,4,6,2,2,1,1,2,4,4,6,6,6,2,3,1,1,2,4,5,6,8,6,7,3,3,1,1,
%U 2,4,5,7,8,10,7,9,3,3,1,1,2,4,5,7,10,10,12,9,11,3,2,1,1,2,4,5,8,10,12,12
%N Triangle T(n,k) = number of partitions of 2*n into n-k prime parts, n>1, 0 <= k <= n-2.
%C Row sums give bisection of A000607.
%e For n=7 the row is [1,1,2,3,1,2] because there are 10 partitions of 14 into prime parts (cf. A000607): 1 with 7 parts: 2+2+2+2+2+2+2; 1 with 6 parts: 2+2+2+2+3+3; 2 with 5 parts: 2+3+3+3+3, 2+2+2+3+5; 3 with 4 parts: 3+3+3+5, 2+2+5+5, 2+2+3+7; 1 with 3 parts: 2+5+7; 2 with 2 parts: 7+7, 3+11.
%Y Cf. A000607, A069259.
%K easy,nonn,tabl
%O 2,10
%A _Vladeta Jovovic_, Mar 10 2002
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