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A111195
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a(n) = 2^(-n) * Sum_{k=0..n} binomial(2*n+1, 2*k+1) * A000364(k).
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0
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1, 2, 5, 26, 269, 4666, 121017, 4370722, 209364537, 12833657010, 979336390669, 91018760056938, 10120101446389765, 1326280083965014634, 202311875122389093761, 35535622109342844729074
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ cosh(Pi/2) * 2^(3*n + 3) * n^(2*n + 1/2) / (Pi^(2*n + 1/2) * exp(2*n)). - Vaclav Kotesovec, Jul 10 2021
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MATHEMATICA
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t = Range[0, 34]!CoefficientList[ Series[ Sec[x], {x, 0, 34}], x]; f[n_] := 2^(-n)*Sum [Binomial[2n + 1, 2k + 1]*t[[2k + 1]], {k, 0, n}]; Table[ f[n], {n, 0, 17}] (* Robert G. Wilson v, Oct 24 2005 *)
Table[Sum[Binomial[2*n + 1, 2*k + 1]*Abs[EulerE[2*k]], {k, 0, n}] / 2^n, {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)
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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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EXTENSIONS
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STATUS
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approved
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