login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292481 p-INVERT of the odd positive integers, where p(S) = 1 - S^3. 1
0, 0, 1, 9, 42, 139, 381, 984, 2685, 8061, 25434, 79695, 242577, 721584, 2131785, 6333633, 18984618, 57194883, 172319157, 517851144, 1552599333, 4651054101, 13939132698, 41810229351, 125475990057, 376585031520, 1129975049169, 3389800055481, 10168040440746 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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 A292480 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 (6, -15, 21, -12, 9)

FORMULA

G.f.: -((x^2 (1 + x)^3)/((-1 + 3 x) (1 - 3 x + 6 x^2 - 3 x^3 + 3 x^4))).

a(n) = 6*a(n-1) - 25*a(n-2) + 21*a(n-3) - 12*a(n-4) + 9*a(n-5) for n >= 6.

MATHEMATICA

z = 60; s = x (x + 1)/(1 - x)^2; p = 1 - s^3;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A005408 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A292481 *)

CROSSREFS

Cf. A005408, A292480.

Sequence in context: A027441 A000971 A061927 * A051923 A180670 A268262

Adjacent sequences:  A292478 A292479 A292480 * A292482 A292483 A292484

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 02 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)