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 A291018 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - 6 S + S^2. 2
 6, 41, 280, 1912, 13056, 89152, 608768, 4156928, 28385280, 193826816, 1323532288, 9037643776, 61712891904, 421401985024, 2877512744960, 19648886079488, 134170986676224, 916176804773888, 6256046544781312, 42718957920059392, 291703291002224640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Suppose s = (c(0), c(1), c(2),...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the "INVERT" transform of s, so that p-INVERT is a generalization of the "INVERT" transform (e.g., A033453). See A291000 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8, -8) FORMULA G.f.: (6 - 7 x)/(1 - 8 x + 8 x^2). a(n) = 8*a(n-1) - 8*a(n-2) n >= 3. MATHEMATICA z = 60; s = x/(1 - x); p = 1 - 6 s + s^2; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000012 *) Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291018 *) CROSSREFS Cf. A000012, A289780, A291000. Sequence in context: A252980 A274997 A015551 * A227214 A049685 A196954 Adjacent sequences: A291015 A291016 A291017 * A291019 A291020 A291021 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 23 2017 STATUS approved

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Last modified December 1 05:02 EST 2022. Contains 358454 sequences. (Running on oeis4.)