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A154558 Triangle read by rows: binomial(n-1,k-1)*A001006(k).

%I A154558 #7 Jul 29 2025 06:44:58
%S A154558 1,1,2,1,4,4,1,6,12,9,1,8,24,36,21,1,10,40,90,105,51,1,12,60,180,315,
%T A154558 306,127,1,14,84,315,735,1071,889,323,1,16,112,504,1470,2856,3556,
%U A154558 2584,835,1,18,144,756,2646,6426,10668,11628,7515,2188
%N A154558 Triangle read by rows: binomial(n-1,k-1)*A001006(k).
%F A154558 Binomial transform of a diagonalized version of the Motzkin sequence:
%F A154558 (A001006 (1, 2, 4, 9, 21, 51,...) as the main diagonal and the rest zeros.)
%F A154558 T(n,n) = A001006(n).
%e A154558 First few rows of the triangle =
%e A154558 1;
%e A154558 1, 2;
%e A154558 1, 4, 4;
%e A154558 1, 6, 12, 9;
%e A154558 1, 8, 24, 36, 21;
%e A154558 1, 10, 40, 90, 105, 51;
%e A154558 1, 12, 60, 180, 315, 306, 127;
%e A154558 1, 14, 84, 315, 735, 1071, 889, 323;
%e A154558 1, 16, 112, 504, 1470, 2856, 3556, 2584, 835;
%e A154558 1, 18, 144, 756, 2646, 6426, 10668, 11628, 7515, 2188;
%e A154558 1, 20, 180, 1080, 4410, 12852, 26670, 38760, 37575, 21880, 5798;
%e A154558 ...
%Y A154558 Cf. A001006, A000245 (row sums), A005843 (column k=2), A046092 (column k=3).
%K A154558 nonn,tabl,easy
%O A154558 1,3
%A A154558 _Gary W. Adamson_, Jan 11 2009