A289800 - OEIS

%I #10 Aug 15 2017 19:54:24

%S 1,4,17,75,336,1517,6879,31276,142439,649431,2963266,13528285,

%T 61785007,282257992,1289734455,5894167695,26939918564,123142940445,

%U 562928407213,2573477722376,11765383864555,53790586563231,245933621620228,1124446028551665,5141224466008849

%N p-INVERT of the central binomial coefficients (A000984), where p(S) = 1 - S - S^2.

%C 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).

%C See A289780 for a guide to related sequences.

%t z = 60; s = x/Sqrt[1 - 4 x]; p = 1 - s - s^2;

%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000984 *)

%t Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289800 *)

%Y Cf. A000984, A289780.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Aug 12 2017