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1, 1, 7, 161, 7631, 607009, 72605303, 12172272321, 2722634203807, 783282749905601, 281751782666559239, 123890976070562785633, 65380371270827869603439, 40779819387085820255904481, 29677003954344675666092048791, 24921035407468294238607282809729
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*E(n+k, n)*binomial(2*n,n-k) where E are the Eulerian numbers A173018. - Peter Luschny, Dec 19 2018
a(n) ~ sqrt(3) * 2^(2*n + 1) * n^(2*n) / exp(2*n + 1). - Vaclav Kotesovec, Dec 19 2018
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MAPLE
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a := n -> add((-1)^(n-k)*combinat:-eulerian1(n+k, n)*binomial(2*n, n-k), k=0..n): seq(a(n), n=0..15); # Peter Luschny, Dec 19 2018
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MATHEMATICA
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E1[n_ /; n >= 0, 0] = 1; E1[n_, k_] /; k < 0 || k > n = 0; E1[n_, k_] := E1[n, k] = (n - k) E1[n - 1, k - 1] + (k + 1) E1[n - 1, k];
a[n_] := Sum[(-1)^(n - k) E1[n + k, n] Binomial[2 n, n - k], {k, 0, n}];
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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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