A098536 Expansion of 1/((1-x)^3 - 9*x^4)^(1/3).

1, 1, 1, 1, 4, 13, 31, 61, 124, 295, 757, 1873, 4402, 10237, 24421, 59701, 146455, 356308, 862810, 2096632, 5127391, 12583513, 30886735, 75775729, 186054142, 457662265, 1127659903, 2781162079, 6862930768, 16945704721, 41876228125

Offset

0,5

Comments

Binomial transform is A098536.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

Recurrence: n*a(n) +(-3*n+2)*a(n-1) +(3*n-4)*a(n-2) +(-n+2)*a(n-3) + 3*(-3*n+8)*a(n-4)=0. - R. J. Mathar, Nov 10 2014

Maple

with(FormalPowerSeries): # requires Maple 2022
re:= subs(n=n-1, FindRE(1/((1-x)^3 - 9*x^4)^(1/3), x, a(n)));
# re = Mathar's recurrence
f:= gfun:-rectoproc({re, a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=4}, a(n), remember): map(f, [$0..30]); # Georg Fischer, Oct 23 2022

Mathematica

CoefficientList[Series[1/((1-x)^3-9*x^4)^(1/3), {x, 0, 40}], x] (* Harvey P. Dale, May 11 2011 *)

Prog

(PARI) x='x+O('x^30); Vec(1/((1-x)^3-9*x^4)^(1/3)) \\ G. C. Greubel, Jan 17 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 30); Coefficients(R!(1/((1-x)^3-9*x^4)^(1/3))); // G. C. Greubel, Jan 17 2018

Crossrefs

Sequence in context: A158842 A100136 A097120 * A216563 A011937 A307304

Adjacent sequences: A098533 A098534 A098535 * A098537 A098538 A098539

Keyword

easy,nonn

Author

Paul Barry, Sep 13 2004

Status

approved