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A342210
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Product of first n secant numbers.
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0
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1, 1, 5, 305, 422425, 21341333425, 57680609034420125, 11499262801779458886142625, 222988094279253104602162884889680625, 536259535797497315015541102040111384540146030625, 198615081477022654229416746174491677406536175668963818424203125
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OFFSET
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0,3
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LINKS
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FORMULA
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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...
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MAPLE
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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:
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MATHEMATICA
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Table[Product[Abs[EulerE[2*k]], {k, 1, n}], {n, 0, 12}]
FoldList[Times, 1, Table[Abs[EulerE[2*n]], {n, 1, 12}]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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