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A133444
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a(n)=sum{k=0..n, C(n,floor(k/2))*(-1)^k*4^(n-k)}.
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1
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1, 3, 14, 57, 246, 1038, 4424, 18777, 79846, 339258, 1442004, 6128202, 26045436, 110691948, 470442924, 1999378137, 8497365126, 36113785698, 153483619604, 652305322542, 2772297736276, 11782265148228, 50074627320864, 212817165231882, 904472953925596
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 5^n . Second binomial transform is A076036 .
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LINKS
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FORMULA
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a(n)=Sum{k, 0<=k<=n} A053121(n,k)*A015521(k+1) = (-1)^n*A127363(n) . G.f.: (1/sqrt(1-4x^2))(1-xc(x^2))/(1-4x*c(x^2)), where c(x) is the g.f. of Catalan numbers A000108 .
Recurrence: 4*n*a(n) = (17*n-8)*a(n-1) + 2*(8*n+1)*a(n-2) - 68*(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*4^(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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