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 A135950 Matrix inverse of triangle A022166. 9
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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 LINKS FORMULA 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). EXAMPLE 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; ... MATHEMATICA 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 *) PROG (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]} CROSSREFS 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 KEYWORD sign,tabl AUTHOR Paul D. Hanna, Dec 08 2007 STATUS approved

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