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A114219 Number triangle (k-(k-1)*0^(n-k))*[k<=n]. 5
1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 4, 1, 0, 1, 2, 3, 4, 5, 1, 0, 1, 2, 3, 4, 5, 6, 1, 0, 1, 2, 3, 4, 5, 6, 7, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Row sums are n(n-1)/2+1 (essentially A000124). Diagonal sums are A114220. First difference triangle of A077028, when this is viewed as a number triangle.

The matrix inverse is

1;

0,1;

0,-1,1;

0,1,-2,1;

0,-2,4,-3,1;

0,6,-12,9,-4,1;

0,-24,48,-36,16,-5,1;

0,120,-240,180,-80,25,-6,1;

0,-720,1440,-1080,480,-150,36,-7,1;

.. apparently related to A208058. - R. J. Mathar, Mar 22 2013

LINKS

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

EXAMPLE

Triangle begins

1;

0, 1;

0, 1, 1;

0, 1, 2, 1;

0, 1, 2, 3, 1;

0, 1, 2, 3, 4, 1;

0, 1, 2, 3, 4, 5, 1;

0, 1, 2, 3, 4, 5, 6, 1;

0, 1, 2, 3, 4, 5, 6, 7, 1;

MAPLE

A114219 := proc(n, k)

    if k < 0 or k > n then

        0;

    elif n = k then

        1;

    else

        k ;

    end if;

end proc: # R. J. Mathar, Mar 22 2013

CROSSREFS

Sequence in context: A065364 A168318 A174203 * A119339 A037835 A116433

Adjacent sequences:  A114216 A114217 A114218 * A114220 A114221 A114222

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 18 2005

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.