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A089093
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Convoluted convolved Fibonacci numbers G_j^(6).
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0
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0, 1, 4, 16, 51, 154, 418, 1098, 2726, 6570, 15308, 34839, 77412, 168882, 361896, 764097, 1590938, 3272640, 6656426, 13403600, 26739028, 52892435, 103806344, 202263470, 391460137, 752923563, 1439737364, 2738144031, 5181025837
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: (z/6)[1/(1-z-z^2)^6-1/(1-z^2-z^4)^3-1/(1-z^3-z^6)^2+1/(1-z^6-z^12)].
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MAPLE
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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(6, j), j=1..40);
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MATHEMATICA
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f[k_] = 1/(1 - z^k - z^(2k))^(6/k); (1/6) (f[1] - f[2] - f[3] + f[6]) + O[z]^30 // CoefficientList[#, z]& (* Jean-François Alcover, Mar 24 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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