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Triangular array E by rows: E(n,k) = number of partitions of n into an even number of parts, the least being k.
2

%I #7 Oct 18 2019 07:58:53

%S 0,1,0,1,0,0,2,1,0,0,2,1,0,0,0,4,1,1,0,0,0,5,1,1,0,0,0,0,8,2,1,1,0,0,

%T 0,0,10,2,1,1,0,0,0,0,0,16,3,1,1,1,0,0,0,0,0,20,4,1,1,1,0,0,0,0,0,0,

%U 29,6,2,1,1,1,0,0,0,0,0,0,37,7,2,1,1,1,0,0,0,0

%N Triangular array E by rows: E(n,k) = number of partitions of n into an even number of parts, the least being k.

%F E(n, k) = O(n-k, k)+O(n-k, k+1)+...+O(n-k, n-k), for 2<=2k<=n, O given by A027185.

%e 0,

%e 1, 0,

%e 1, 0, 0,

%e 2, 1, 0, 0,

%e 2, 1, 0, 0, 0,

%e 4, 1, 1, 0, 0, 0,

%e 5, 1, 1, 0, 0, 0, 0,

%e 8, 2, 1, 1, 0, 0, 0, 0,

%e 10, 2, 1, 1, 0, 0, 0, 0, 0,

%e 16, 3, 1, 1, 1, 0, 0, 0, 0, 0,

%e 20, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0,

%e 29, 6, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0,

%e 37, 7, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,

%Y Cf. A027185.

%K nonn,tabl

%O 1,7

%A _Clark Kimberling_