|
%I #9 Dec 09 2017 11:08:42
%S 0,1,7,33,145,552,1959,6435,20039,59345,168862,463385,1233082,3191530,
%T 8061718,19919613,48255611,114812555,268730241,619603435,1409012926,
%U 3163562545,7019590107,15405769535,33467218583,72013318602,153577843509
%N Sign twisted convoluted convolved Fibonacci numbers H_j^(10).
%H P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>
%F G.f.: (z/10)[1/(1-z-z^2)^10+1/(1-z^2-z^4)^5-1/(1-z^5-z^10)^2-1/(1-z^10-z^20)].
%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(10,j),j=1..35);
%t terms = 27; r = 10; f[z_] := -1/(1 - z - z^2);
%t W = (z/r)*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}]+ O[z]^(terms+1);
%t CoefficientList[W, z] // Rest (* _Jean-François Alcover_, Dec 09 2017, from Maple *)
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Dec 05 2003
%E Edited by _Emeric Deutsch_, Mar 06 2004
|
