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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

Table of n, a(n) for n=1..27.

P. Moree, Convoluted convolved Fibonacci numbers

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);

CoefficientList[W, z] // Rest (* Jean-Fran├žois Alcover, Dec 09 2017, from Maple *)

CROSSREFS

Sequence in context: A297392 A263479 A073375 * A120009 A074087 A297592

Adjacent sequences:  A089094 A089095 A089096 * A089098 A089099 A089100

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2003

EXTENSIONS

Edited by Emeric Deutsch, Mar 06 2004

STATUS

approved

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Last modified August 14 07:59 EDT 2020. Contains 336477 sequences. (Running on oeis4.)