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A106194 Triangle read by rows, generated from binomial transforms of odd numbers.

%I A106194 #15 Jun 02 2017 21:33:34
%S A106194 1,4,1,12,5,1,32,17,6,1,80,49,23,7,1,192,129,72,30,8,1,448,321,201,
%T A106194 102,38,9,1,1024,769,522,303,140,47,10,1,2304,1793,1291,825,443,187,
%U A106194 57,11,1,5120,4097,3084,2116,1268,630,244,68,12,1
%N A106194 Triangle read by rows, generated from binomial transforms of odd numbers.
%C A106194 Appending the binomial transform of the natural numbers, (A001792: 1, 3, 8, 20, 48...) to A106194 as a leftmost column creates triangle A055249.
%C A106194 Placing zeros into the offset spaces, column 1: 0, 1, 5, 17, 49...; is the binomial transform of 0, 1, 3, 5...; and alternatively the binomial transform of 0, 0, 1, 2, 3...
%C A106194 n-th column is the binomial transform of 1, 3, 5...prefaced by n zeros. n-th column is alternatively the binomial transform of 1, 2, 3...prefaced by (n+1) zeros. The triangle of A106194 is identical to the binomial transform (of natural numbers, prefaced with zeros) triangle: A055249, deleting the leftmost column.
%e A106194 First few rows of the triangle are:
%e A106194 1;
%e A106194 4, 1;
%e A106194 12, 5, 1;
%e A106194 32, 17, 6, 1;
%e A106194 80, 49, 23, 7, 1;
%e A106194 192, 129, 72, 30, 8, 1;
%e A106194 448, 321, 201, 102, 38, 9, 1;
%e A106194 ...
%Y A106194 Cf. A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055249.
%K A106194 nonn,tabl
%O A106194 0,2
%A A106194 _Gary W. Adamson_, Apr 24 2005