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A024719
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a(n) = (1/3)*(2 + Sum_{k=0..n} C(3k,k)).
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1
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1, 2, 7, 35, 200, 1201, 7389, 46149, 291306, 1853581, 11868586, 76380826, 493606726, 3201081874, 20821158234, 135776966762, 887393271311, 5811082966886, 38119865826421, 250447855600321, 1647729357535486, 10854207824989831, 71581930485576631, 472560922429972951, 3122648143126315651
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} C(k-n,2n-2k). - Paul Barry, Mar 15 2010
G.f.: (1-2*g)/((3*g-1)*(g^3-2*g^2+g-1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011
Conjecture: 2*n*(2*n-1)*a(n) + (-31*n^2 + 29*n - 6)*a(n-1) +3*(3*n-1)*(3*n-2)*a(n-2) = 0. - R. J. Mathar, Sep 29 2012
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MATHEMATICA
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Table[Sum[Binomial[k-n, 2n-2k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)
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PROG
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(PARI) a(n)=sum(k=0, n, binomial(k-n, 2*(n-k)) ); \\ Joerg Arndt, May 04 2013
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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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