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A360602
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a(n) = ((2*n + 1)! / n!)^2 / (n + 1).
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0
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1, 18, 1200, 176400, 45722880, 18441561600, 10685567692800, 8414884558080000, 8646761377013760000, 11237331085567082496000, 18020592759036666839040000, 34953943088278121445457920000, 80662945588334126412595200000000, 218412210097326433146332774400000000
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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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a(n) = CatalanNumber(n) * (2*n)! * (2*n + 1)^2.
a(n) ~ (4*n/e)^(2*n)*(8*n - 2/3).
Sum_{n>=0} 1/a(n) = 1/2 + StruveL(0, 1/2)*Pi/2 + StruveL(1, 1/2)*Pi/4, where StruveL is the modified Struve function.
Sum_{n>=0} (-1)^n/a(n) = 1/2 + StruveH(0, 1/2)*Pi/2 - StruveH(1, 1/2)*Pi/4, where StruveH is the Struve function. (End)
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MAPLE
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a := n -> ((2*n + 1)! / n!)^2 / (n + 1):
seq(a(n), n = 0..13);
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MATHEMATICA
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a[n_] := ((2*n + 1)!/n!)^2/(n + 1); Array[a, 14, 0] (* Amiram Eldar, Mar 02 2023 *)
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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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