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%I #11 Dec 09 2017 11:18:32
%S 0,1,6,28,115,418,1396,4367,12925,36542,99385,261365,667501,1661325,
%T 4041025,9629631,22526515,51820065,117401263,262291425,578530315,
%U 1261055274,2718900535,5802916275,12268722487,25711496512,53441431933,110223868969,225695796260
%N Convoluted convolved Fibonacci numbers G_j^(9).
%H Colin Barker, <a href="/A089096/b089096.txt">Table of n, a(n) for n = 1..1000</a>
%H P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>
%F G.f.: (z/9)[1/(1-z-z^2)^9-1/(1-z^3-z^6)^3].
%p with(numtheory): f := z->1/(1-z-z^2): m := proc(r,j) d := divisors(r): W := (1/r)*z*sum(mobius(d[i])*f(z^d[i])^(r/d[i]),i=1..nops(d)): Wser := simplify(series(W,z=0,80)): coeff(Wser,z^j) end: seq(m(9,j),j=1..40);
%t CoefficientList[(z/9)(1/(1-z-z^2)^9 - 1/(1-z^3-z^6)^3) + O[z]^28, z] // Rest (* _Jean-François Alcover_, Dec 09 2017 *)
%o (PARI) concat(0, Vec(x^2*(1 - x)^2*(1 + x)^2*(1 - 3*x + 3*x^2 + 4*x^3 - 9*x^4 - 3*x^5 + 11*x^6 + 3*x^7 - 9*x^8 - 4*x^9 + 3*x^10 + 3*x^11 + x^12) / ((1 - x - x^2)^9*(1 - x^3 - x^6)^3) + O(x^40))) \\ _Colin Barker_, Dec 09 2017
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Dec 05 2003
%E Edited by _Emeric Deutsch_, Mar 06 2004
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