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A104728 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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.

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 *)

CROSSREFS

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

Sequence in context: A168077 A173536 A014717 * A058093 A164032 A122846

Adjacent sequences:  A104725 A104726 A104727 * A104729 A104730 A104731

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Mar 20 2005

EXTENSIONS

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

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)