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A291033
p-INVERT of the positive integers, where p(S) = 1 - 6*S.
2
6, 48, 378, 2976, 23430, 184464, 1452282, 11433792, 90018054, 708710640, 5579667066, 43928625888, 345849340038, 2722866094416, 21437079415290, 168773769227904, 1328753074407942, 10461250826035632, 82361253533877114, 648428777444981280, 5105068966025973126
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 A290890 for a guide to related sequences.
FORMULA
G.f.: 6/(1 - 8 x + x^2).
a(n) = 8*a(n-1) - a(n-2).
a(n) = 6*A001090(n) for n >= 1.
MATHEMATICA
z = 60; s = x/(1 - x)^2; p = 1 - 6 s;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291033 *)
CROSSREFS
Sequence in context: A052625 A326888 A326895 * A155130 A250164 A264083
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 19 2017
STATUS
approved