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Search: id:A158359
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| A158359 |
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Triangle read by rows, charpolys of nxn matrices with [1; 1,2; 1,2,3;...] in the lower half and the rest 1's. |
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+0
2
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| 1, 1, 1, 1, 3, 1, 1, 6, 7, 2, 1, 10, 25, 23, 6, 1, 15, 65, 123, 98, 24, 1, 21, 140, 448, 713, 514, 120, 1, 28, 266, 1288, 3401, 4792, 3204, 720, 1, 36, 462, 3150, 12417, 28599, 36748, 23148, 5040, 1, 45, 750, 6846, 37617, 127935, 265540, 317132, 190224, 40320
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Determinant of nxn matrix = (n-1)!. Row sums = A000522: (1, 2, 5, 16, 65, 326, 1957,...). Product of n-th degree charpoly roots = (n-1)!
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FORMULA
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Triangle read by rows, charpolys of nxn matrices with [1; 1,2; 1,2,3;...] in the lower half and the rest 1's.
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EXAMPLE
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First few charpolys are:
1;
x - 1;
x^2 - 3x + 1;
x^3 - 6x^2 + 7x - 2;
x^4 - 10x^3 + 25x^2 - 23x + 6;
x^5 - 15x^4 + 65x^3 - 123x^2 + 98x - 24;
x^6 - 21x^5 + 140x^4 - 448x^3 + 713x^2 - 514x + 120;
x^7 - 28x^6 + 266x^5 - 1288x^4 + 3401x^3 - 4792x^2 + 3204x - 720;
x^8 - 36x^7 + 462x^6 - 3150x^5 + 12417x^4 - 28599x^3 + 36748x^2 - 23148x + 5040;
x^9 - 45x^8 + 750x^7 - 6846x^6 + 37617x^5 - 127935x^4 + 265540x^3 - 317132x^2 + 190224x - 40320;
x^10 - 55x^9 + 1155x^8 - 13596x^7 + 99231x^6 - 466488x^5 + 1416955x^4 - 2706992x^3 + 3044412x^2 - 1752336x + 362880
...
Example: 3x3 matrix = [1,1,1; 1,2,1; 1,2,3]; charpoly = x^3 - 6x^2 + 7x - 2,
determinant = 2.
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CROSSREFS
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Cf. A000522
Sequence in context: A008278 A056858 A137251 this_sequence A046716 A123354 A120247
Adjacent sequences: A158356 A158357 A158358 this_sequence A158360 A158361 A158362
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Mar 17 2009
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