

A291181


pINVERT of the positive integers, where p(S) = 1  8*S.


2



8, 80, 792, 7840, 77608, 768240, 7604792, 75279680, 745192008, 7376640400, 73021211992, 722835479520, 7155333583208, 70830500352560, 701149669942392, 6940666199071360, 68705512320771208, 680114457008640720, 6732439057765635992, 66644276120647719200
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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 pINVERT 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 pINVERT is a generalization of the "INVERT" transform (e.g., A033453).
See A290890 for a guide to related sequences.


LINKS



FORMULA

G.f.: 8/(1  10 x + x^2).
a(n) = 10*a(n1)  a(n2).


MATHEMATICA

z = 60; s = x/(1  x)^2; p = 1  8 s;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291181 *)
LinearRecurrence[{10, 1}, {8, 80}, 30] (* Harvey P. Dale, Jul 31 2023 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



