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 A185331 Riordan array ((1-x+x^2)/(1+x^2), x/(1+x^2)). 1
 1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 0, 2, -2, -1, 1, -1, 1, 3, -3, -1, 1, 0, -3, 3, 4, -4, -1, 1, 1, -1, -6, 6, 5, -5, -1, 1, 0, 4, -4, -10, 10, 6, -6, -1, 1, -1, 1, 10, -10, -15, 15, 7, -7, -1, 1, 0, -5, 5, 20, -20, -21, 21, 8, -8, -1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Triangle T(n,k), read by rows, given by (-1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. LINKS G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened FORMULA T(n,k) = T(n-1,k-1) - T(n-2,k), T(0,0) = 1, T(0,1) = -1, T(0,2) = 0. G.f.: (1-x+x^2)/(1-y*x+x^2). Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A184334(n), A163805(n), A000007(n), A028310(n), A025169(n-1), A005320(n) (n>0) for x = -1, 0, 1, 2, 3, 4 respectively. T(n,n) = 1, T(n+1,n) = -1, T(n+2,n) = -n, T(n+3,n) = n+1, T(n+4,n) = n(n+1)/2 = A000217(n). T(2n,2k) = (-1)^(n-k) * A128908(n,k), T(2n+1,2k+1) = -T(2n+1,2k) = A129818(n,k), T(2n+2,2k+1) = (-1)*A053122(n,k). - Philippe Deléham, Feb 09 2012 EXAMPLE Triangle begins:    1;   -1,  1;    0, -1,   1;    1, -1,  -1,   1;    0,  2,  -2,  -1,   1;   -1,  1,   3,  -3,  -1,   1;    0, -3,   3,   4,  -4,  -1,   1;    1, -1,  -6,   6,   5,  -5,  -1,  1;    0,  4,  -4, -10,  10,   6,  -6, -1,  1;   -1,  1,  10, -10, -15,  15,   7, -7, -1,  1;    0, -5,   5,  20, -20, -21,  21,  8, -8, -1,  1;    1, -1, -15,  15,  35, -35, -28, 28,  9, -9, -1, 1; MATHEMATICA CoefficientList[Series[CoefficientList[Series[(1 - x + x^2)/(1 - y*x + x^2), {x, 0, 10}], x], {y, 0, 10}], y] // Flatten (* G. C. Greubel, Jun 27 2017 *) CROSSREFS Cf. A206474 (unsigned version). Cf. A007318, A053122, A078812, A085478, A128908, A129818, Sequence in context: A165031 A286634 A099245 * A206474 A211999 A175025 Adjacent sequences:  A185328 A185329 A185330 * A185332 A185333 A185334 KEYWORD easy,sign,tabl AUTHOR Philippe Deléham, Feb 08 2012 STATUS approved

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)