A089111 - OEIS

%I #20 Mar 25 2018 10:29:55

%S 8,19,37,64,102,154,222,309,418,552,715,910,1141,1412,1727,2091,2508,

%T 2983,3521,4127,4807,5566,6410,7345,8377,9513,10759,12122,13609,15227,

%U 16984,18887,20944,23163,25552,28120,30875,33826,36982,40352,43946

%N Convoluted convolved Fibonacci numbers G_6^(r).

%H Vincenzo Librandi, <a href="/A089111/b089111.txt">Table of n, a(n) for n = 1..2000</a>

%H P. Moree, <a href="https://arxiv.org/abs/math/0311205">Convoluted convolved Fibonacci numbers</a>, arXiv:math/0311205 [math.CO], 2003.

%F Empirical g.f.: -x*(2*x^8-8*x^7+12*x^6-7*x^5-2*x^3+9*x^2-13*x+8) / ((x-1)^5*(x^4+x^3+x^2+x+1)). - _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,6),r=1..65);

%t f[z_] = 1/(1-z-z^2); m[r_, j_] := (1/r)*z*DivisorSum[r, MoebiusMu[#] * f[z^#]^(r/#)&] // SeriesCoefficient[#, {z, 0, j}]&; Table[m[r, 6], {r, 1, 41}] (* _Jean-François Alcover_, Mar 25 2018, translated from Maple *)

%K nonn

%O 1,1

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

%E Edited by _Emeric Deutsch_, Mar 06 2004