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A159605
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E.g.f: Sum_{n>=1} a(n)*x^(2n-1)/(2n-1)! = Series_Reversion of e.g.f. S(x) of A159601.
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1
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1, 3, 63, 3465, 363825, 62214075, 15740160975, 5524796502225, 2569030373534625, 1528573072253101875, 1132672646539548489375, 1022803399825212285905625, 1105650475211054481063980625, 1409704355894094463356575296875
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Product_{k=1..n} (2k-3)(4k-5).
a(n) ~ Gamma(1/4) * 2^(3*n - 5/2) * n^(2*n - 7/4) / (sqrt(Pi) * exp(2*n)). - Vaclav Kotesovec, Nov 19 2023
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EXAMPLE
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E.g.f.: A(x) = x + 3*x^3/3! + 63*x^5/5! + 3465*x^7/7! +...
A(S(x)) = x where S(x) = Sum_{n>=1} A159601(n)*x^(2n-1)/(2n-1)! :
S(x) = x - 3*x^3/3! + 27*x^5/5! - 441*x^7/7! + 11529*x^9/9! +...
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MATHEMATICA
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Table[Product[(2k-3)(4k-5), {k, n}], {n, 15}] (* Harvey P. Dale, Jan 31 2023 *)
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PROG
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(PARI) a(n)=prod(k=1, n, (2*k-3)*(4*k-5))
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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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