A144061 Eigentriangle generated from A109128, row sums = expansion of {2(exp(x)-1)}

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, 1, 17, 142, 1002, 5522, 23594, 75818, 172530, 241638, 89918

Offset

1,5

Comments

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.

Links

Table of n, a(n) for n=1..55.

Formula

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,...).

Example

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.

Crossrefs

A109128, Cf. A001861

Sequence in context: A330784 A198876 A033878 * A085792 A108123 A105954

Adjacent sequences: A144058 A144059 A144060 * A144062 A144063 A144064

Keyword

nonn,tabl

Author

Gary W. Adamson & Roger L. Bagula, Sep 09 2008

Status

approved