A342210 Product of first n secant numbers.

1, 1, 5, 305, 422425, 21341333425, 57680609034420125, 11499262801779458886142625, 222988094279253104602162884889680625, 536259535797497315015541102040111384540146030625, 198615081477022654229416746174491677406536175668963818424203125

Offset

0,3

Links

Table of n, a(n) for n=0..10.

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

Cf. A000364.

Sequence in context: A158996 A042763 A323012 * A300425 A300687 A300610

Adjacent sequences: A342207 A342208 A342209 * A342211 A342212 A342213

Keyword

nonn

Author

Vaclav Kotesovec, Mar 05 2021

Status

approved