1,5

Row sums = A001861: (1, 2, 6, 22, 94, 454, 2430,...) = expansion of {2(exp(x)-1)}

Right border = A001861 shifted: (1, 1, 2, 6, 22, 94,...).

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

T(n,k) = A109128(n,k)*A001861(k-1).

A109128 = (2*binomial(n,k) - 1): (1; 1,1; 1,3,1; 1,5,5,1;...).

A001861(k-1) = A001861 shifted one place, = (1, 1, 2, 6, 22, 94, 454,...).

First few rows of the triangle =

1;

1, 1;

1, 3, 2;

1, 5, 10, 6;

1, 7, 22, 42, 22;

1, 9, 38, 114, 198, 94;

1, 11, 58, 234, 638, 1034, 454;

1, 13, 82, 414, 1518, 3854, 5902, 2430;

1, 15, 110, 666, 3058, 10434, 24970, 36450, 14214;

...

Example: row 3 = (1, 5, 10, 6) = termwise products of (1, 5, 5, 1) and (1, 1, 2, 6), where (1, 5, 5, 1) = row 3 of triangle A109128 and (1, 1, 2, 6) = the first 4 terms of A001861 shifted.

A109128, Cf. A001861

Sequence in context: A114597 A050165 A033878 this_sequence A085792 A108123 A105954

Adjacent sequences: A144058 A144059 A144060 this_sequence A144062 A144063 A144064

nonn,tabl

Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Sep 09 2008