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A213953
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Triangle by rows, inverse of A208891.
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1
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1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 1, 1, -2, -1, 1, -2, 5, 0, -3, -1, 1, -9, 5, 10, -2, -4, -1, 1, -9, -21, 25, 15, -5, -5, -1, 1, 50, -105, -11, 62, 19, -9, -6, -1, 1, 267, -141, -301, 56, 119, 21, -14, -7, -1, 1, 413, 777
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,13
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LINKS
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FORMULA
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Inverse of triangle A208891, Pascal's triangle matrix with an appended right border of 1's.
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EXAMPLE
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Triangle starts:
1;
-1, 1
0, -1, 1
1, -1, -1, 1;
1, 1, -2, -1, 1;
-2, 5, 0, -3, -1, 1;
-9, 5, 10, -2, -4, -1, 1;
-9, -21, 25, 15, -5, -5, -1, 1;
50, -105, -11, 62, 19, -9, -6, -1, 1;
267, -141, -301, 56, 119, 21, -14, -7, -1, 1;
413, 777, -1040, -566, 226, 198, 20, -20, -8, -1, 1;
...
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MAPLE
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if n <0 or k<0 or k>n then
0;
elif n = k then
1 ;
else
binomial(n-1, k) ;
end if;
end proc:
local A, row, col ;
A := Matrix(n, n) ;
for row from 1 to n do
for col from 1 to n do
A[row, col] := A208891(row-1, col-1) ;
end do:
end do:
LinearAlgebra[MatrixInverse](A) ;
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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