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A133443
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a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-1)^k*3^(n-k).
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1
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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
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 4^n. Second binomial transform is A076035.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A053121(n,k)*A015518(k+1) = (-1)^n*A127362(n). G.f.: (1/sqrt(1-4*x^2))*(1-x*c(x^2))/(1-3*x*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
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MATHEMATICA
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Table[Sum[Binomial[n, Floor[k/2]]*(-1)^k*3^(n-k), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 20 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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