A289800 p-INVERT of the central binomial coefficients (A000984), where p(S) = 1 - S - S^2.

1, 4, 17, 75, 336, 1517, 6879, 31276, 142439, 649431, 2963266, 13528285, 61785007, 282257992, 1289734455, 5894167695, 26939918564, 123142940445, 562928407213, 2573477722376, 11765383864555, 53790586563231, 245933621620228, 1124446028551665, 5141224466008849

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. A000984, A289780.

Programs

Mathematica

z = 60; s = x/Sqrt[1 - 4 x]; p = 1 - s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000984 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289800 *)