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A208057
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Triangle by rows, generated from the odd integers and related to A000165.
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3
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1, 1, 1, 4, 3, 1, 24, 18, 5, 1, 192, 144, 40, 7, 1, 1920, 1440, 400, 70, 9, 1, 23040, 17280, 4800, 840, 108, 11, 1, 322560, 241920, 67200, 11760, 1512, 154, 13, 1, 5160960, 3870720, 1075200, 188160, 24192, 2464, 208, 15, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Row sums = A000165, the double factorial numbers: (1, 2, 8, 48, 384,...).
Left border = A002866 and the eigensequence of the odd integers prefaced with a 1.
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LINKS
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FORMULA
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Eigentriangle of triangle A158405 (odd integers in every row: (1, 3, 5,...); the inverse of:
1;
-1, 1;
-1, -3, 1;
-1, -3, -5, 1;
-1, -3, -5, -7, 1;
...
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EXAMPLE
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First few rows of the triangle =
1;
1, 1;
4, 3, 1;
24, 18, 5, 1;
192, 144, 40, 7, 1;
1920, 1440, 400, 70, 9, 1;
23040, 17280, 4800, 840, 108, 11, 1;
322560, 241920, 67200, 11760, 1512, 154, 13, 1;
...
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MAPLE
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T:= proc(n) option remember; local M;
M:= (Matrix(n+1, (i, j)-> `if`(i=j, 1, `if`(i>j, -2*j+1, 0)))^(-1));
seq(M[n+1, k], k=1..n+1)
end:
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MATHEMATICA
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T[n_] := T[n] = Module[{M}, M = Table[If[i == j, 1, If[i>j, -2*j+1, 0]], {i, 1, n+1 }, {j, 1, n+1}] // Inverse; M[[n+1]]]; Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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