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%I #16 Jul 10 2021 06:13:57
%S 1,2,5,26,269,4666,121017,4370722,209364537,12833657010,979336390669,
%T 91018760056938,10120101446389765,1326280083965014634,
%U 202311875122389093761,35535622109342844729074
%N a(n) = 2^(-n) * Sum_{k=0..n} binomial(2*n+1, 2*k+1) * A000364(k).
%F 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
%t 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 *)
%t 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 *)
%Y Cf. A000364, A103327, A308715.
%K easy,nonn
%O 0,2
%A _Philippe Deléham_, Oct 24 2005
%E More terms from _Robert G. Wilson v_, Oct 24 2005
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