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.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12, -58, 144, -195, 144, -58, 12, -1)
FORMULA
G.f.: (4 - 30 x + 88 x^2 - 125 x^3 + 88 x^4 - 30 x^5 + 4 x^6)/(1 - 3 x + x^2)^4.
a(n) = 12*a(n-1) - 58*a(n-2) + 144*a(n-3) - 195*a(n-4) + 144*a(n-5) - 58*a(n-6) + 12*a(n-7) - a(n-8).
(a(n)) is the p-INVERT of (1,1,1,1,1...) using p(S) = (1 - S - S^2)^4.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 18 2017
STATUS
approved