A289810 p-INVERT of A081696, where p(S) = 1 - S - S^2.

1, 3, 10, 37, 141, 548, 2155, 8543, 34062, 136393, 547957, 2207144, 8908901, 36021499, 145853606, 591277797, 2399421839, 9745388640, 39611178893, 161109065899, 655647568024, 2669558849029, 10874316446699, 44313536385428, 180644362403905, 736631134007651

Offset: 0

Author

Clark Kimberling, Aug 12 2017

Keywords

• nonn
• easy

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 A289780 for a guide to related sequences.

Crossrefs

Cf. A081696, A289780.

Programs

Mathematica

z = 60; s = x/(x + Sqrt[1 - 4*x]); p = 1 - s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A081696 shifted *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289810 *)