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%I #5 Feb 24 2019 10:58:48
%S 1,3,1260,471517200,550527639742080000,
%T 5190428828598394601457507916800,
%U 850896871373200757118814347241271815302935592960,4613713947380451287616678748167888181805816329703795184496036199596032
%N Hankel transform of median Euler numbers A000657.
%F a(n)=Product{k=0..n, ((k+1)(4k+1)(4k+3)floor((2k+3)/2))^(n-k)}.
%F a(n) ~ sqrt(Gamma(1/4)) * 2^(2*n^2 + 7*n/2 + 9/8) * n^(n*(2*n+3) + 47/48) * Pi^(n + 3/4) / (A^(7/4) * exp(3*n*(n+1) - 7/48)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Feb 24 2019
%t Table[Product[((k+1)*(4*k+1)*(4*k+3)*Floor[(2*k+3)/2])^(n-k), {k,0,n}], {n,0,10}] (* _Vaclav Kotesovec_, Feb 24 2019 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 30 2010
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