

A157905


Triangle read by rows, T(n,k) = A000055(nk) * (A157904 * 0^(nk))


2



1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 2, 1, 2, 4, 8, 3, 2, 2, 4, 8, 17, 6, 3, 4, 4, 8, 17, 36, 11, 6, 6, 8, 8, 17, 36, 78, 23, 11, 12, 12, 16, 17, 36, 78, 170, 47, 23, 22, 24, 24, 34, 36, 78, 170, 375, 106, 47, 46, 44, 48, 51, 72, 78, 170, 375, 833
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OFFSET

0,6


COMMENTS

Row sums = A157904: (1, 2, 4, 8, 17, 36, 78, 170, 375,...). As a property of eigentriangles, sum of nth row terms = rightmost term of next row. Left border = A000055.


LINKS

Table of n, a(n) for n=0..65.


FORMULA

Triangle read by rows, T(n,k) = A000055(nk) * (A157904 * 0^(nk)). A000055(nk) = an infinite lower triangular matrix with A000055 in every column: (1, 1, 1, 1, 2, 3, 6, 11, 23,...). (A157904 * 0^(nk)) = a matrix with A157904 as the diagonal and the rest zeros.


EXAMPLE

First few rows of the triangle =
1;
1, 1;
1, 1, 2;
1, 1, 2, 4;
2, 1, 2, 4, 8;
3, 2, 2, 4, 8, 17;
6, 3, 4, 4, 8, 17, 36;
11, 6, 6, 8, 8, 17, 36, 78;
23, 11, 12, 12, 16, 17, 36, 78, 170;
47, 23, 22, 24, 24, 34, 36, 78, 170, 375;
106, 47, 46, 44, 48, 51, 72, 78, 170, 375, 833;
235, 106, 94, 92, 88, 102, 108, 156, 170, 375, 833, 1870;
...
Row 5 = (3, 2, 2, 4, 8, 17) = termwise products of (3, 2, 1, 1, 1, 1) and (1, 1, 2, 4, 8, 17).


CROSSREFS

Cf. A000055, A157904
Sequence in context: A097853 A160266 A023504 * A260931 A293819 A027113
Adjacent sequences: A157902 A157903 A157904 * A157906 A157907 A157908


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Mar 08 2009


STATUS

approved



