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%I #11 Mar 12 2016 15:29:22
%S 1,2,0,2,0,1,2,0,2,1,2,0,2,2,1,2,0,2,4,2,1,2,0,2,4,2,4,1,2,0,2,6,2,6,
%T 2,2,2,0,2,6,2,8,2,6,2,2,0,2,8,2,8,2,12,4,2,2,0,2,8,2,10,2,14,6,8,2,2,
%U 0,2,10,2,10,2,18,8,14,6,3,2,0,2,10,2,12,2,18,10,20,10,10,3,2,0,2,12,2,12,2,22,12,22,14,20,10,3,2,0,2,12,2,14,2,22,16,26,16,26,20,12,4
%N Triangle, read by rows, of integer partitions of n by kernel size k.
%C Row sum is A000041.
%C Sum k*T(n,k) = A208914(n).
%C The kernel of an integer partition is the intersection of its Ferrers diagram and of the Ferrers diagram of its conjugate.
%C Its size is between 1 (for an all-1 partition) and n (for a self-conjugate partition).
%e Triangle begins:
%e 1;
%e 2, 0;
%e 2, 0, 1;
%e 2, 0, 2, 1;
%e 2, 0, 2, 2, 1;
%e 2, 0, 2, 4, 2, 1;
%e 2, 0, 2, 4, 2, 4, 1;
%e 2, 0, 2, 6, 2, 6, 2, 2;
%e 2, 0, 2, 6, 2, 8, 2, 6, 2;
%e 2, 0, 2, 8, 2, 8, 2, 12, 4, 2;
%e 2, 0, 2, 8, 2, 10, 2, 14, 6, 8, 2;
%e 2, 0, 2, 10, 2, 10, 2, 18, 8, 14, 6, 3;
%e 2, 0, 2, 10, 2, 12, 2, 18, 10, 20, 10, 10, 3;
%e 2, 0, 2, 12, 2, 12, 2, 22, 12, 22, 14, 20, 10, 3;
%e 2, 0, 2, 12, 2, 14, 2, 22, 16, 26, 16, 26, 20, 12, 4;
%Y Cf. A218904, A218905, A218906.
%Y Cf. A115720, A115994, A246581.
%Y Main diagonal gives A000700.
%K nonn,tabl
%O 1,2
%A _Olivier Gérard_, Nov 08 2012
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