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A262394
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a(n) = (1/n)*Sum_{k=1..n} k*binomial(n,k-1)*binomial(2*n,n-k).
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4
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1, 4, 20, 110, 637, 3808, 23256, 144210, 904475, 5722860, 36463440, 233646504, 1504152860, 9721421440, 63040282096, 409972529754, 2672860120455, 17464206951100, 114330456032100, 749760805916430
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*B'(x) + B(x) - B'(x)/B(x) - 1, where B(x) is g.f. of A001764.
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MATHEMATICA
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Table[Sum[k Binomial[n, k-1] Binomial[2n, n-k], {k, n}]/n, {n, 30}] (* Michael De Vlieger, Sep 21 2015 *)
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PROG
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(Maxima)
a(n):=sum(k*binomial(n, k-1)*binomial(2*n, n-k), k, 1, n)/n;
(PARI) a(n)=sum(k=1, n, (k*binomial(n, k-1)*binomial(2*n, n-k))/n) \\ Anders Hellström, Sep 21 2015
(Magma) [(n+2)*Binomial(3*n, n)/(3*(2*n+1)): n in [1..30]]; // G. C. Greubel, Nov 09 2022
(SageMath) [(n+2)*binomial(3*n, n)/(3*(2*n+1)) for n in range(1, 31)] # G. C. Greubel, Nov 09 2022
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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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