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A166359
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Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357.
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2
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1, 3, 15, 197, 6909, 459383, 48252699, 7299708105, 1499523879481, 401147660278507, 135421121289695655, 56285769483090611085, 28237152577765405343285, 16821061018350834178553055
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OFFSET
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0,2
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COMMENTS
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Aeration of this sequence gives the diagonal sums of A166357.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} C(n+k,2k)*A166356(k).
a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / exp(2*n). - Vaclav Kotesovec, Aug 17 2018
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MATHEMATICA
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Table[1 + Sum[Binomial[n + k, 2*k] * ((2*k-1)! + (2*k-2)!), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 17 2018 *)
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PROG
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(PARI) a(n)={1 + sum(k=1, n, binomial(n + k, 2*k) * ((2*k-1)! + (2*k-2)!))} \\ Andrew Howroyd, Aug 17 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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