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%I #6 Mar 23 2022 01:07:35
%S 1,1,2,1,4,1,1,6,3,4,1,8,6,16,1,1,10,10,40,5,6,1,12,15,80,15,36,1,1,
%T 14,21,140,35,126,7,8,1,16,28,224,70,336,28,64,1,1,18,36,336,126,756,
%U 84,288,9,10
%N A007318 * (a diagonalized version of A124625).
%C Row sums = A129954: (1, 3, 6, 14, 32, 72, 160, ...).
%F Binomial transform of an infinite lower triangular matrix, with (1, 2, 1, 4, 1, 6, ...) in the main diagonal and zeros elsewhere.
%e First few rows of the triangle:
%e 1;
%e 1, 2;
%e 1, 4, 1;
%e 1, 6, 3, 4;
%e 1, 8, 6, 16, 1;
%e 1, 10, 10, 40, 5, 6;
%e 1, 12, 15, 80, 15, 36, 1;
%e ...
%Y Cf. A129954.
%K nonn,tabl
%O 1,3
%A _Gary W. Adamson_, Sep 29 2007