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A135950
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Matrix inverse of triangle A022166.
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9
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1, -1, 1, 2, -3, 1, -8, 14, -7, 1, 64, -120, 70, -15, 1, -1024, 1984, -1240, 310, -31, 1, 32768, -64512, 41664, -11160, 1302, -63, 1, -2097152, 4161536, -2731008, 755904, -94488, 5334, -127, 1, 268435456, -534773760, 353730560, -99486720, 12850368, -777240, 21590, -255, 1
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history;
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OFFSET
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0,4
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COMMENTS
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A022166 is the triangle of Gaussian binomial coefficients [n,k] for q = 2.
The coefficient [x^k] of product_{i=1..n} (x-2^(i-1)). - Roger L. Bagula, Mar 20 2009
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LINKS
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Table of n, a(n) for n=0..44.
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FORMULA
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Unsigned column 0 equals A006125(n) = 2^{n(n-1)/2}. Unsigned column 1 equals A127850(n) = (2^n-1)*2^(n(n-1)/2)/(2^(n-1)). Row sums equal 0^n. Unsigned row sums equal A028361(n) = Product_{k=0..n} (1+2^k).
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EXAMPLE
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Triangle begins:
1;
-1, 1;
2, -3, 1;
-8, 14, -7, 1;
64, -120, 70, -15, 1;
-1024, 1984, -1240, 310, -31, 1;
32768, -64512, 41664, -11160, 1302, -63, 1;
-2097152, 4161536, -2731008, 755904, -94488, 5334, -127, 1; ...
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MATHEMATICA
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p[x_, n_] = Product[x - 2^(i - 1), {i, 1, n}];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
Table[Apply[Plus, CoefficientList[ExpandAll[p[x, n]], x]], {n, 0, 10}]; (* Roger L. Bagula, Mar 20 2009 *)
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PROG
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(PARI) {T(n, k)=local(q=2, A=matrix(n+1, n+1, n, k, if(n>=k, if(n==1|k==1, 1, prod(j=n-k+1, n-1, 1-q^j)/prod(j=1, k-1, 1-q^j))))^-1); A[n+1, k+1]}
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CROSSREFS
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Cf. A022166; A006125, A028361, A127850, A135951 (central terms), A158474.
Sequence in context: A098435 A096294 A157963 * A202063 A200016 A147557
Adjacent sequences: A135947 A135948 A135949 * A135951 A135952 A135953
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna, Dec 08 2007
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STATUS
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approved
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