

A145677


Triangle T(n,m) read by rows: T(n,0) =1; T(n,n) =n, n>0; T(n,k) =0, 0<k<n1 .


4



1, 1, 1, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11
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OFFSET

0,6


COMMENTS

The first column is all1, the diagonals are the integers, the rest is zero.
The vector of (1, 1, 2, 5, 16, 65, 326,...), which is 1 followed by A000522,
is an eigenvector of the matrix: 1+ sum_{k=1..n} T(n,k)*A000522(k1) = A000522(n).


LINKS

Table of n, a(n) for n=0..77.


FORMULA

T(n,k) = A158821(n,nk).
1+ sum_{k= 1..n} T(n,k) *(k1) = A002061(n).


EXAMPLE

First few rows of the triangle:
1;
1, 1;
1, 0, 2;
1, 0, 0, 3;
1, 0, 0, 0, 4;
1, 0, 0, 0, 0, 5;
1, 0, 0, 0, 0, 0, 6;
1, 0, 0, 0, 0, 0, 0, 7;
1, 0, 0, 0, 0, 0, 0, 0, 8;
1, 0, 0, 0, 0, 0, 0, 0, 0, 9;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10;


CROSSREFS

Cf. A002061, A000522.
Sequence in context: A063658 A237053 A209777 * A128229 A132013 A105820
Adjacent sequences: A145674 A145675 A145676 * A145678 A145679 A145680


KEYWORD

nonn,tabl,easy


AUTHOR

Gary W. Adamson & Roger L. Bagula, Mar 28 2009


EXTENSIONS

Edited by R. J. Mathar, Oct 02 2009


STATUS

approved



