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 A206831 Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 1
 1, 1, 1, -1, 0, 1, -1, -3, -1, 1, 1, 0, -4, -2, 1, 1, 5, 4, -4, -3, 1, -1, 0, 9, 10, -3, -4, 1, -1, -7, -9, 9, 17, -1, -5, 1, 1, 0, -16, -28, 2, 24, 2, -6, 1, 1, 9, 16, -16, -54, -14, 30, 6, -7, 1, -1, 0, 25, 60, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Riordan array ((1+x)/(1+x^2), x*(1-x)/(1+x^2)). Antidiagonal sums are A010892(n). LINKS Indranil Ghosh, Rows 0..100, flattened FORMULA T(n,k) = T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n>1. G.f.: (1+x)/(1-y*x+(1+y)*x^2). Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A057077(n), (-1)^n*A078050(n) for x = -1, 0, 1 respectively. EXAMPLE Triangle begins : 1 1, 1 -1, 0, 1 -1, -3, -1, 1 1, 0, -4, -2, 1 1, 5, 4, -4, -3, 1 -1, 0, 9, 10, -3, -4, 1 -1, -7, -9, 9, 17, -1, -5, 1 1, 0, -16, -28, 2, 24, 2, -6, 1 1, 9, 16, -16, -54, -14, 30, 6, -7, 1 -1, 0, 25, 60, 10, -80, -40, 34, 11, -8, 1 MATHEMATICA nmax=10; Flatten[CoefficientList[Series[CoefficientList[Series[(1 + x)/(1 - y*x + (1 + y)*x^2), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 10 2017 *) CROSSREFS Cf. A129267, A007318, A147703, A147721 Cf. A057077, A087960 Sequence in context: A110245 A230003 A136093 * A304222 A134108 A176851 Adjacent sequences:  A206828 A206829 A206830 * A206832 A206833 A206834 KEYWORD easy,sign,tabl AUTHOR Philippe Deléham, Feb 13 2012 STATUS approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)