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A246582
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G.f.: x^((k^2+k)/2)/(mul(1-x^i,i=1..k)*mul(1+x^r,r=1..oo)) with k = 3.
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3
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0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, -1, 1, -2, 1, -3, 1, -4, 2, -5, 3, -6, 5, -7, 7, -8, 10, -10, 13, -12, 17, -15, 21, -19, 26, -24, 31, -30, 38, -38, 45, -47, 54, -58, 64, -71, 77, -86, 91, -103, 109, -124, 129, -147, 154, -174, 182, -205, 216, -241, 254, -282, 300, -330, 351, -384, 412, -447, 480, -519, 560, -602, 649, -696, 753, -805
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OFFSET
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0,14
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REFERENCES
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Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70, Eq. 3, with k=3.
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LINKS
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FORMULA
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a(n) ~ (-1)^n * 3^(1/4) * exp(sqrt(n/6)*Pi) / (2^(13/4)*Pi*n^(1/4)). - Vaclav Kotesovec, Mar 12 2016
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MAPLE
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fSp:=proc(k) local a, i, r;
a:=x^((k^2+k)/2)/mul(1-x^i, i=1..k);
a:=a/mul(1+x^r, r=1..101);
series(a, x, 101);
seriestolist(%);
end;
fSp(3);
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MATHEMATICA
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nmax = 100; CoefficientList[Series[x^6/((1-x)*(1-x^2)*(1-x^3)) * Product[1/(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 11 2016 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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