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 A113287 Triangle T, read by rows, where row n of T equals row n of matrix (n+1)-th power of triangle A112555. 5
 1, 2, 1, -3, 0, 1, 4, 4, 4, 1, -5, -10, -10, 0, 1, 6, 18, 24, 12, 6, 1, -7, -28, -49, -42, -21, 0, 1, 8, 40, 88, 104, 72, 24, 8, 1, -9, -54, -144, -216, -198, -108, -36, 0, 1, 10, 70, 220, 400, 460, 340, 160, 40, 10, 1, -11, -88, -319, -682, -946, -880, -550, -220, -55, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Remarkably, the matrix logarithm (A113290) is an integer triangle. Matrix m-th power of A112555 = I + m*(A112555 - I) where I = identity matrix. LINKS Table of n, a(n) for n=0..65. FORMULA G.f.: A(x, y) = 1/(1-x*y) + x*(x+2)/((1-x*y)^2*(1+x+x*y)^2). EXAMPLE Triangle begins: 1; 2,1; -3,0,1; 4,4,4,1; -5,-10,-10,0,1; 6,18,24,12,6,1; -7,-28,-49,-42,-21,0,1; 8,40,88,104,72,24,8,1; -9,-54,-144,-216,-198,-108,-36,0,1; 10,70,220,400,460,340,160,40,10,1; ... PROG (PARI) {T(n, k)=local(x=X+X*O(X^n), y=Y+Y*O(Y^k)); polcoeff(polcoeff(1/(1-x*y)+x*(x+2)/((1-x*y)^2*(1+x+x*y)^2), n, X), k, Y)} CROSSREFS Cf. A112555, A113288 (inverse), A113290 (log), A113291, A072374. Sequence in context: A347351 A355342 A130026 * A195665 A096798 A158902 Adjacent sequences: A113284 A113285 A113286 * A113288 A113289 A113290 KEYWORD sign,tabl AUTHOR Paul D. Hanna, Oct 23 2005 STATUS approved

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Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)