A104728 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.

1, 9, 4, 30, 18, 7, 70, 48, 27, 10, 135, 100, 66, 36, 13, 231, 180, 130, 84, 45, 16, 364, 294, 225, 160, 102, 54, 19, 540, 448, 357, 270, 190, 120, 63, 22, 765, 648, 532, 420, 315, 220, 138, 72, 25, 1045, 900, 756, 616, 483, 360, 250, 156, 81, 28, 1386, 1210, 1035, 864, 700, 546, 405, 280, 174, 90, 31

Offset: 1

Author

Gary W. Adamson, Mar 20 2005

Keywords

• nonn
• easy
• tabl

Comments

The triangle is defined as the matrix product A * B, A = [1; 1, 4; 1, 4, 7;...]; B = [1; 2, 1; 3, 2, 1;...]; both infinite lower triangular matrices with the rest of the terms zeros.

Examples

			The first few rows of the triangle are:
1;
9,    4;
30,   18,   7;
70,   48,   27,   10;
135,  100,  66,   36,   13;
231,  180,  130,  84,   45,  16;
364,  294,  225,  160,  102, 54,  19;
540,  448,  357,  270,  190, 120, 63,  22;
765,  648,  532,  420,  315, 220, 138, 72,  25;
1045, 900,  756,  616,  483, 360, 250, 156, 81,  28;
1386, 1210, 1035, 864,  700, 546, 405, 280, 174, 90,  31;
1794, 1584, 1375, 1170, 972, 784, 609, 450, 310, 192, 99, 34, etc.
		

Crossrefs

Cf. A051798 (row sums), A007586, A002414 (column 1).

Programs

Maple

A104728 := proc(n)
        (k-1-n)*(k-2-n)*(k-2+2*n)/2 ;
end proc:
seq(seq(A104728(n,k),k=1..n),n=1..14) ; # R. J. Mathar, Nov 07 2011

Mathematica

Table[(k-1-n)(k-2-n)(k-2+2n)/2,{n,20},{k,n}]//Flatten (* Harvey P. Dale, Dec 25 2018 *)

Extensions

Name contributed by R. J. Mathar, Nov 07 2011