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A049610
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a(n) = Sum_{k=0..floor(n/2)} k*binomial(n,2*k) = floor(n*2^(n-3)).
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5
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0, 0, 1, 3, 8, 20, 48, 112, 256, 576, 1280, 2816, 6144, 13312, 28672, 61440, 131072, 278528, 589824, 1245184, 2621440, 5505024, 11534336, 24117248, 50331648, 104857600, 218103808, 452984832, 939524096, 1946157056, 4026531840, 8321499136, 17179869184, 35433480192
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OFFSET
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0,4
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COMMENTS
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Essentially same as A001792, except for leading zeros, which motivate the existence of this sequence on its own.
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LINKS
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FORMULA
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G.f.: x^2*( 1 + 2*x*U(0) ) where U(k) = 1 + (k+1)/(2 - 8*x/(4*x + (k+1)/U(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 19 2012
Sum_{n>=2} 1/a(n) = 8*log(2) - 4. - Amiram Eldar, Feb 14 2023
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MATHEMATICA
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CoefficientList[Series[x^2*(1 - x)/(1 - 2*x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 09 2013 *)
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PROG
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(PARI) a(n)=n<<(n-3)
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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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