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A339001
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a(n) = (-1)^n * Sum_{k=0..n} (-n)^k * binomial(n,k) * Catalan(k).
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3
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1, 0, 5, 89, 2481, 93274, 4450645, 258297570, 17689681345, 1397903887808, 125286890408901, 12562851683433765, 1393925069404093105, 169595051215441936902, 22454465186157134883285
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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) = n! * [x^n] exp((2*n-1)*x) * (BesselI(0,2*n*x) - BesselI(1,2*n*x)). - Ilya Gutkovskiy, Feb 01 2021
a(n) ~ exp(-1/4) * 4^n * n^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Feb 14 2021
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MATHEMATICA
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a[0] = 1; a[n_] := (-1)^n * Sum[(-n)^k * Binomial[n, k] * CatalanNumber[k], {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Feb 01 2021 *)
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PROG
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(PARI) {a(n) = (-1)^n*sum(k=0, n, (-n)^k*binomial(n, k)*(2*k)!/(k!*(k+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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