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A336728
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a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.
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2
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1, 1, -1, 1, 9, -174, 2575, -38219, 588833, -9274418, 141253551, -1739881142, -753419447, 1379742127908, -83720072007585, 4059017293956301, -184613801568558975, 8254420480122200214, -369177108304219471457, 16608406418618863804990, -750673988803431836351799
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-n)^k * (n+1)^(n-k) * binomial(n,k) * binomial(n+k,n)/(k+1).
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MATHEMATICA
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a[0] = 1; a[n_] := Sum[(-n)^(n - k) * Binomial[n, k] * Binomial[n , k - 1], {k, 1, n}] / n; Array[a, 21, 0] (* Amiram Eldar, Aug 02 2020 *)
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PROG
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(PARI) {a(n) = if(n==0, 1, sum(k=1, n, (-n)^(n-k)*binomial(n, k)*binomial(n, k-1))/n)}
(PARI) {a(n) = sum(k=0, n, (-n)^k*(n+1)^(n-k)*binomial(n, k)*binomial(n+k, n)/(k+1))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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