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A185087
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a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A000108(k+1).
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1
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1, 1, 3, 5, 12, 24, 55, 119, 272, 612, 1411, 3247, 7565, 17667, 41561, 98099, 232696, 553784, 1322813, 3169065, 7614583, 18342921, 44294991, 107200829, 259983346, 631718606, 1537737567, 3749440151, 9156561590, 22394270034, 54845701243
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OFFSET
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0,3
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COMMENTS
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Hankel transform is A008619(n+1) (counting numbers doubled).
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LINKS
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FORMULA
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G.f.: (1-x-2x^2-sqrt(1-2x-3x^2+4x^3))/(2x^4).
G.f.: 1/(1-x-2x^2/(1-(1/2)x^2/(1-x-(3/2)x^2/(1-(2/3)x^2/(1-x-(4/3)x^2/(1-(3/4)x^2/(1-... (continued fraction).
a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*if(n-k-j>=0, A001006(n-k-j),0)}}.
Conjecture: (n+4)*a(n) -(2*n+5)*a(n-1) -3*(n+1)*a(n-2) +2*(2*n-1)*a(n-3)=0. - R. J. Mathar, Nov 16 2011
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MATHEMATICA
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CoefficientList[Series[(1 - x - 2*x^2 - Sqrt[1 - 2 x - 3 x^2 + 4 x^3])/(2*x^4), {x, 0, 50}], x] (* G. C. Greubel, Jun 22 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1-x-2*x^2-sqrt(1-2*x-3*x^2+4*x^3))/(2*x^4)) \\ G. C. Greubel, Jun 22 2017
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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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