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Triangle generated from binomial transforms of (1; 2, 3; 3, 4, 5; ...).
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%I #12 Feb 08 2022 08:13:00

%S 1,2,1,3,5,1,4,7,8,1,5,9,16,11,1,6,11,20,30,14,1,7,13,24,44,49,17,1,8,

%T 15,28,52,88,73,20,1,9,17,32,60,103,159,102,23,1

%N Triangle generated from binomial transforms of (1; 2, 3; 3, 4, 5; ...).

%F Take antidiagonals of an array generated by taking binomial transforms of (1; 2, 3; 3, 4, 5; 4, 5, 6, 7; ...)

%e First few rows of the array are:

%e 1, 1, 1, 1, ...

%e 2, 5, 8, 11, ...

%e 3, 7, 16, 30, ...

%e 4, 9, 20, 44, ...

%e ...

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 3, 5, 1;

%e 4, 7, 8, 1;

%e 5, 9, 16, 11, 1;

%e 6, 11, 20, 30, 14, 1;

%e 7, 13, 24, 44, 49, 17, 1;

%e ...

%e Example: The diagonal 3, 7, 16, 30, 49, ... (third row of the array) = binomial transform of (3, 4, 5, 0, 0, 0, ...).

%K nonn,tabl,more

%O 1,2

%A _Gary W. Adamson_, May 16 2006