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A125170 Binomial transform of an infinite lower triangular matrix with (1,1,2,4,8,...) in every column and the rest zeros. Let the left column = A007051, then for k > 1, T(n,k) = (n-1,k) + (n-1,k-1).

%I A125170 #12 Feb 14 2022 03:54:56
%S A125170 1,2,1,5,3,1,14,8,4,1,41,22,12,5,1,122,63,34,17,6,1,365,185,97,51,23,
%T A125170 7,1,1094,550,282,148,74,30,8,1,3281,1644,832,430,222,104,38,9,1
%N A125170 Binomial transform of an infinite lower triangular matrix with (1,1,2,4,8,...) in every column and the rest zeros. Let the left column = A007051, then for k > 1, T(n,k) = (n-1,k) + (n-1,k-1).
%e A125170 (5,3) = 34 = 12 + 22 = (4,3) + (4,2).
%e A125170 First few rows of the triangle:
%e A125170     1;
%e A125170     2,  1;
%e A125170     5,  3,  1;
%e A125170    14,  8,  4,  1;
%e A125170    41, 22, 12,  5, 1;
%e A125170   122, 63, 34, 17, 6, 1;
%e A125170   ...
%Y A125170 Cf. A000244 (row sums), A007051 (left border).
%K A125170 nonn,tabl
%O A125170 0,2
%A A125170 _Gary W. Adamson_, Nov 22 2006
%E A125170 Edited by _N. J. A. Sloane_, Oct 07 200