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 A049610 Sum( k*binomial(n,2*k), 0 <= k <= n/2) = floor( n*2^(n-3) ). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Essentially same as A001792, except for leading zeros, which motivate the existence of this sequence on its own. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA G.f. x^2*(1-x)/(1-2*x)^2. - Sergei N. Gladkovskii, Oct 18 2012 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 MATHEMATICA CoefficientList[Series[x^2*(1 - x)/(1 - 2*x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 09 2013 PROG (PARI) a(n)=n<<(n-3) CROSSREFS Cf. A189162, A189390, A189391. Sequence in context: A143662 A151975 A001792 * A168150 A018795 A018794 Adjacent sequences:  A049607 A049608 A049609 * A049611 A049612 A049613 KEYWORD nonn,easy AUTHOR M. F. Hasler, Jan 25 2012 STATUS approved

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