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 A133443 a(n)=sum{k=0..n, C(n,floor(k/2))*(-1)^k*3^(n-k)}. 1
 1, 2, 8, 24, 84, 272, 920, 3040, 10180, 33840, 112968, 376224, 1254696, 4181088, 13939248, 46459584, 154873860, 516229040, 1720795880, 5735921440, 19119861304, 63732624672, 212442552528, 708140901184, 2360471473384, 7868234639072, 26227455730640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Hankel transform is 4^n . Second binomial transform is A076035 . LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n)=Sum{k, 0<=k<=n} A053121(n,k)*A015518(k+1) = (-1)^n*A127362(n) . G.f.: (1/sqrt(1-4x^2))(1-xc(x^2))/(1-3x*c(x^2)), where c(x) is the g.f. of Catalan numbers A000108 . Recurrence: 3*n*a(n) = 2*(5*n-3)*a(n-1) + 4*(3*n-1)*a(n-2) - 40*(n-2)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012 a(n) ~ 2*10^n/3^(n+1) . - Vaclav Kotesovec, Oct 20 2012 MATHEMATICA Table[Sum[Binomial[n, Floor[k/2]]*(-1)^k*3^(n-k), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 20 2012 *) CROSSREFS Sequence in context: A063727 A085449 A127362 * A094038 A007223 A106189 Adjacent sequences:  A133440 A133441 A133442 * A133444 A133445 A133446 KEYWORD nonn AUTHOR Philippe Deléham, Nov 26 2007, Dec 07 2007 EXTENSIONS More terms from Vincenzo Librandi, May 25 2013 STATUS approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)