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%I #9 Mar 05 2021 09:21:47
%S 1,1,5,305,422425,21341333425,57680609034420125,
%T 11499262801779458886142625,222988094279253104602162884889680625,
%U 536259535797497315015541102040111384540146030625,198615081477022654229416746174491677406536175668963818424203125
%N Product of first n secant numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SecantNumber.html">Secant Number</a>.
%F a(n) = Product_{k=1..n} A000364(k).
%F a(n) ~ c * 2^(n*(2*n+5)) * n^(n^2 + 3*n/2 + 11/24) / (Pi^(n*(2*n+3)/2) * exp(3*n*(n+1)/2)), where c = 2.5721331354145587505860723440097968952290343671042591815289106254690586572...
%p b:= proc(u, o) option remember;
%p `if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
%p end:
%p a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(2*n, 0)) end:
%p seq(a(n), n=0..12); # _Alois P. Heinz_, Mar 05 2021
%t Table[Product[Abs[EulerE[2*k]], {k,1,n}], {n, 0, 12}]
%t FoldList[Times, 1, Table[Abs[EulerE[2*n]], {n, 1, 12}]]
%Y Cf. A000364.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 05 2021
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