A089113 - OEIS

%I #12 Apr 01 2018 21:09:40

%S 13,34,77,146,259,418,654,967,1396,1946,2665,3555,4683,6048,7728,9729,

%T 12141,14966,18319,22198,26732,31928,37930,44740,52533,61306,71251,

%U 82376,94891,108798,124344,141525,160608,181602,204795,230189,258115

%N Convoluted convolved Fibonacci numbers G_7^(r).

%H P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>

%F Empirical g.f.: -x*(2*x^14 -4*x^13 -2*x^12 +6*x^11 +2*x^10 -5*x^9 -8*x^8 +10*x^7 +12*x^6 -6*x^5 -5*x^4 +3*x^3 +4*x^2 -8*x -13) / ((x -1)^6 * (x +1)^3 * (x^2 -x +1) * (x^2 +x +1)^2). - _Colin Barker_, Jul 31 2013

%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(r,7),r=1..65);

%t terms = 40; f[z_] = 1/(1-z-z^2); m[r_, j_] := SeriesCoefficient[(1/r)*z* DivisorSum[r, MoebiusMu[#]*f[z^#]^(r/#)&], {z, 0, j}]; Table[m[r, 7], {r, 1, terms}] (* _Jean-François Alcover_, Apr 01 2018 *)

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 05 2003

%E Edited by _Emeric Deutsch_, Mar 06 2004