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A133805
Triangle read by rows: A007318 * A133566 * A133080.
2
1, 2, 1, 4, 3, 1, 7, 6, 4, 1, 11, 10, 11, 5, 1, 16, 15, 25, 15, 6, 1, 22, 21, 50, 35, 22, 7, 1, 29, 28, 91, 70, 63, 28, 8, 1, 37, 36, 154, 126, 154, 84, 37, 9, 1, 46, 45, 246, 210, 336, 210, 129, 45, 10, 1, 56, 55, 375, 330, 672, 462, 375, 165, 56, 11, 1, 67, 66, 550, 495, 1254, 924, 957, 495, 231, 66, 12, 1
OFFSET
1,2
COMMENTS
Row sums = A133806: (1, 3, 8, 18, 38, 78, 318, ...).
Left column = A000124.
FORMULA
Binomial transform of (A133566 * A133080) where (A133566 * A133080) = an infinite lower triangular matrix with (1,1,1,...) in the main and subdiagonals and (1,0,1,0,1,...) in the subsubdiagonal.
EXAMPLE
First few rows of the triangle:
1;
2, 1;
4, 3, 1;
7, 6, 4, 1;
11, 10, 11, 5, 1;
16, 15, 25, 15, 6, 1;
22, 21, 50, 35, 22, 7, 1;
29, 28, 91, 70, 63, 28, 8, 1;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Sep 23 2007
EXTENSIONS
a(21) = 1 inserted and more terms from Georg Fischer, Jun 08 2023
STATUS
approved