A174826 Hankel transform of median Euler numbers A000657.
1, 3, 1260, 471517200, 550527639742080000, 5190428913555819988454400000000, 850897011688550259860209488988778496000000000000, 4613713285873452716084822982464795709127827429408768000000000000000000
Offset: 0
Programs
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Mathematica
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 *)
Formula
a(n) = Product_{k=0..n} ((k+1)*(4k+1)*(4k+3)*floor((2k+3)/2))^(n-k).
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
Extensions
a(5) and following corrected by Georg Fischer, Jan 18 2024