|
|
A089097
|
|
Convoluted convolved Fibonacci numbers G_j^(10).
|
|
0
|
|
|
0, 1, 6, 33, 141, 552, 1946, 6435, 20001, 59345, 168760, 463385, 1232823, 3191530, 8061092, 19919613, 48254154, 114812555, 268726954, 619603435, 1409005702, 3163562545, 7019574578, 15405769535, 33467185837, 72013318602, 153577775602
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
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)].
|
|
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(m(10, j), j=1..40);
|
|
MATHEMATICA
|
terms = 27; r = 10; f[z_] := 1/(1 - z - z^2);
W = (z/r)*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}]+ O[z]^(terms+1);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|