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A104728
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Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.
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1
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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; internal format)
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OFFSET
| 1,2
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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.
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EXAMPLE
| The first few rows of the triangle are:
1;
9, 4;
30, 18, 7;
70, 48, 27, 10;
...
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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
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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
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2005
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EXTENSIONS
| Name contributed by R. J. Mathar, Nov 07 2011
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