1,6

Row sums = A000084: (1, 2, 4, 10, 24, 66,...).

Right border = A000084 shifted: (1, 1, 2, 4, 10, 24,...)

Left border = A001572: (1, 1, 1, 3, 5, 17, 41,...).

A000084 = the INVERT transform of A001572.

Sum of n-th row terms = rightmost term of next row.

Triangle read by rows, T(n,k) = A001572(n-k+1) * (A000084 * 0^(n-k)), 1<=k<=n.

Given an A001572 "decrescendo" triangle: (1; 1,1; 1,1,1; 3,1,1,1; 5,3,1,1,1;...), where A001572 begins: (1, 1, 1, 3, 5, 17, 41, 127,...); apply termwise products of the decrescendo triangle row terms to A000084 terms: (1, 2, 4, 10, 24, 66, 180, 522,...).

First few rows of the triangle =

1;

1, 1;

1, 1, 2;

3, 1, 2, 4;

5, 3, 2, 4, 10;

17, 5, 6, 4, 10, 24;

41, 17, 10, 12, 10, 24, 66;

127, 41, 34, 20, 30, 24, 66, 180;

365, 127, 82, 68, 50, 72, 66, 180, 522;

1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532;

...

Example: row 5 = (5, 3, 2, 4, 10) = termwise products of (5, 3, 1, 1, 1) and (1, 1, 2, 4, 10).

A000084, Cf. A001572

Sequence in context: A035459 A048232 A163256 this_sequence A166871 A152736 A139246

Adjacent sequences: A144959 A144960 A144961 this_sequence A144963 A144964 A144965

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008