OFFSET
1,1
LINKS
P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.
Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.
FORMULA
Empirical g.f.: -x*(x^7-4*x^6+8*x^5-12*x^4+15*x^3-13*x^2+9*x-5) / ((x-1)^4*(x^2+1)^2). - Colin Barker, Jul 31 2013
MAPLE
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((-1)^r*m(r, 5), r=1..60);
MATHEMATICA
f[z_] = -1/(1 - z - z^2);
m[r_, j_] := (1/r)*z*DivisorSum[r, MoebiusMu[#]*f[z^#]^(r/#)&] // SeriesCoefficient[#, {z, 0, j}]&;
Table[(-1)^r*m[r, 5], {r, 1, 60}] (* Jean-François Alcover, Mar 27 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 05 2003
EXTENSIONS
Edited by Emeric Deutsch, Mar 06 2004
STATUS
approved