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A342210 Product of first n secant numbers. 0
1, 1, 5, 305, 422425, 21341333425, 57680609034420125, 11499262801779458886142625, 222988094279253104602162884889680625, 536259535797497315015541102040111384540146030625, 198615081477022654229416746174491677406536175668963818424203125 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)