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A036829
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a(n) = Sum_{k=0..n-1} C(3*k,k)*C(3*n-3*k-2,n-k-1).
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3
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0, 1, 7, 48, 327, 2221, 15060, 102012, 690519, 4671819, 31596447, 213633696, 1444131108, 9760401756, 65957919496, 445671648228, 3011064814455, 20341769686311, 137412453018933, 928188965638464, 6269358748632207, 42343731580741821
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OFFSET
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0,3
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REFERENCES
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M. Petkovsek et al., A=B, Peters, 1996, p. 97.
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LINKS
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FORMULA
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G.f.: (g-g^2)/(3*g-1)^2 where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011
Recurrence: 8*(n-1)*(2*n-1)*a(n) = 6*(36*n^2-81*n+49)*a(n-1) - 81*(3*n-5)*(3*n-4)*a(n-2). - Vaclav Kotesovec, Nov 19 2012
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MATHEMATICA
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Table[Sum[Binomial[3k, k]Binomial[3n-3k-2, n-k-1], {k, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Jan 10 2012 *)
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PROG
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(Haskell)
a036829 n = sum $ map
(\k -> (a007318 (3*k) k) * (a007318 (3*n-3*k-2) (n-k-1))) [0..n-1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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