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A241204
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Expansion of (1 + 2*x)^2/(1 - 2*x)^2.
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4
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1, 8, 32, 96, 256, 640, 1536, 3584, 8192, 18432, 40960, 90112, 196608, 425984, 917504, 1966080, 4194304, 8912896, 18874368, 39845888, 83886080, 176160768, 369098752, 771751936, 1610612736, 3355443200, 6979321856, 14495514624, 30064771072, 62277025792
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 4*a(n-1)-4*a(n-2) for n>2. - Colin Barker, Apr 23 2014
Sum_{n>=1} 1/a(n) = log(2)/4.
Sum_{n>=1} (-1)^(n+1)/a(n) = log(3/2)/4. (End)
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MAPLE
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MATHEMATICA
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Table[2^(n+2)*n + Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 07 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 41); Coefficients(R!((1+2*x)^2/(1-2*x)^2));
(PARI) Vec((2*x+1)^2/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Apr 22 2014
(Sage)
if i==0: return 1
else: return 2^(2+i)*i;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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