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A000658
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Strehl's sequence "C_n^(3)".
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3
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1, 4, 68, 1732, 51076, 1657904, 57793316, 2117525792, 80483121028, 3147565679824, 125937573689968, 5133632426499152, 212530848994367524, 8914634034287235856, 378138515326996979168, 16196097181014298854032
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OFFSET
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0,2
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REFERENCES
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Volker Strehl, Binomial identities - combinatorial and algorithmic aspects. Trends in discrete mathematics. Discrete Math. 136 (1994), no. 1-3, 309-346.
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LINKS
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FORMULA
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Sum binomial(n, k)^2 * binomial(2k, k)^2 * binomial(2k, n-k); k=0..n.
a(n) ~ 7^(2*n+5/2) / (20 * sqrt(15) * Pi^2 * n^2). - Vaclav Kotesovec, Mar 09 2014
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MAPLE
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MATHEMATICA
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Table[Sum[Binomial[n, k]^2 Binomial[2k, k]^2 Binomial[2k, n-k], {k, 0, n}], {n, 0, 25}] (* Harvey P. Dale, Oct 19 2011 *)
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PROG
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(PARI) a(n)=sum(k=1, n, binomial(n, k)^2 * binomial(2k, k)^2 * binomial(2k, n-k)) \\ Charles R Greathouse IV, Sep 19 2014
(Haskell)
a000658 n = sum $ map c3 [0..n] where
c3 k = (a007318' n k)^2 * (a007318' (2*k) k)^2 * a007318' (2*k) (n-k)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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