OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Secant Number.
FORMULA
a(n) = Product_{k=1..n} A000364(k).
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...
MAPLE
b:= proc(u, o) option remember;
`if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(2*n, 0)) end:
seq(a(n), n=0..12); # Alois P. Heinz, Mar 05 2021
MATHEMATICA
Table[Product[Abs[EulerE[2*k]], {k, 1, n}], {n, 0, 12}]
FoldList[Times, 1, Table[Abs[EulerE[2*n]], {n, 1, 12}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 05 2021
STATUS
approved