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A052277
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a(n) = (4n+2)!/2^(2n+1).
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7
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1, 90, 113400, 681080400, 12504636144000, 548828480360160000, 49229914688306352000000, 8094874872198213459360000000, 2252447502438386084347676160000000, 997586474354936812896742294502400000000, 669959124447288464805194190141921792000000000
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OFFSET
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0,2
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LINKS
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FORMULA
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sin(x)*sinh(x) = Sum_{n>=0} (-1)^n*x^(4n+2)/a(n). - Benoit Cloitre, Feb 02 2002
a(n) = Pi^(4n)/Zeta({4}_n) where ({4}_n) is the standard multiple zeta values notation for (4, ..., 4) where the multiplicity of 4 is n. - Roudy El Haddad, Feb 19 2022
Sum_{n>=0} 1/a(n) = (cosh(sqrt(2)) - cos(sqrt(2)))/2.
Sum_{n>=0} (-1)^n/a(n) = sin(1)*sinh(1). (End)
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MATHEMATICA
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Table[(4n+2)!/2^(2n+1), {n, 0, 10}] (* Amiram Eldar, Feb 25 2022 *)
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PROG
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CROSSREFS
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Cf. A002432 (denominators of zeta(2*n)/Pi^(2*n)).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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