OFFSET
0,2
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 (3, 0, -4)
FORMULA
G.f.: (3 x - 5 x^2)/((1 + x) (-1 + 2 x)^2).
a(n) = 3*a(n-1) - 4*a(n-3) for n >= 4.
a(n) = (16*((-1)^(1+n) + 2^n) + 3*2^n*n) / 18. - Colin Barker, Aug 24 2017
MATHEMATICA
PROG
(PARI) concat(0, Vec(x*(3 - 5*x) / ((1 + x)*(1 - 2*x)^2) + O(x^40))) \\ Colin Barker, Aug 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 24 2017
STATUS
approved