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 A104041 Triangular matrix T, read by rows, such that column k is equal (in absolute value) to row (k-1) in the matrix inverse T^-1 (with extrapolated zeros) for k>0, with T(n,n)=1 (n>=0) and T(n,n-1)=-n (n>=1). 2
 1, -1, 1, 0, -2, 1, 0, 2, -3, 1, 0, 0, 4, -4, 1, 0, 0, -4, 8, -5, 1, 0, 0, 0, -8, 12, -6, 1, 0, 0, 0, 8, -20, 18, -7, 1, 0, 0, 0, 0, 16, -32, 24, -8, 1, 0, 0, 0, 0, -16, 48, -56, 32, -9, 1, 0, 0, 0, 0, 0, -32, 80, -80, 40, -10, 1, 0, 0, 0, 0, 0, 32, -112, 160, -120, 50, -11, 1, 0, 0, 0, 0, 0, 0, 64, -192, 240, -160, 60, -12, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1,0,-1,0, 1,0,-1,0, ...}. Absolute row sums form A038754. Let A(x,y) be the g.f. of T and B(x,y) be the g.f. of T^-1; then B(x,y)=1+x*y*A(-1/y,-x*y^2) and A(x,y)=(B(-x^2*y,-1/x)-1)/(x*y). LINKS FORMULA G.f.: A(x, y) = (1-x+x*y)/(1+2*x^2*y-x^2*y^2). EXAMPLE Rows of T begin: 1; -1,1; 0,-2,1; 0,2,-3,1; 0,0,4,-4,1; 0,0,-4,8,-5,1; 0,0,0,-8,12,-6,1; 0,0,0,8,-20,18,-7,1; ... The matrix inverse T^-1 equals triangle A104040: 1; 1,1; 2,2,1; 4,4,3,1; 8,8,8,4,1; 16,16,20,12,5,1; 32,32,48,32,18,6,1; 64,64,112,80,56,24,7,1; ... the rows of T^-1 equal columns of T in absolute value. PROG (PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); polcoeff(polcoeff((1-X+X*Y)/(1+2*X^2*Y-X^2*Y^2), n, x), k, y)} CROSSREFS Cf. A104040, A038754. Sequence in context: A031135 A037181 A051070 * A104402 A261897 A131084 Adjacent sequences:  A104038 A104039 A104040 * A104042 A104043 A104044 KEYWORD sign,tabl AUTHOR Paul D. Hanna, Mar 02 2005 STATUS approved

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)