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A262407
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a(n) = Sum_{k=0..n-1} C(n,k+1)*C(n,k)*C(n-1,k).
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1
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0, 1, 4, 24, 152, 1010, 6912, 48328, 343408, 2471274, 17966360, 131717960, 972488640, 7223061040, 53925450880, 404400203280, 3044645475296, 23002424245754, 174324246314184, 1324800580881952, 10093304926771600, 77073430602848316, 589761299099196224
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ 8^n/(sqrt(3)*Pi*n) as n -> oo.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n,
((21*n^3-49*n^2+30*n-8)*a(n-1)+
(8*(n-1))*(n-2)*(3*n-1)*a(n-2))/
((3*n-4)*(n+1)*(n-1)))
end:
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MATHEMATICA
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f[n_]:=HypergeometricPFQ[{-n, -n, -n}, {1, 1}, -1]; a[n_]:=n^2 (f[n] + 4 f[n - 1])/(3 n^2 + 3 n); Array[a, 25] (* Vincenzo Librandi, Sep 22 2015 *)
Table[Sum[Binomial[n, k+1]Binomial[n, k]Binomial[n-1, k], {k, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Apr 09 2021 *)
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PROG
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(PARI) a(n)=sum(k=0, n-1, binomial(n, k+1)*binomial(n, k)*binomial(n-1, k))
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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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