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Search: id:A158111
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| A158111 |
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E.g.f.: sm^-1(x) = Sum_{n>=0} a(n)*x^(3n+1)/(3n+1)!; a(n) = coefficient of x^(3n+1)/(3n+1)! in the Maclaurin expansion of the inverse of the Dixon elliptic function sm(x,0). |
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1
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| 1, 4, 400, 179200, 216832000, 552487936000, 2554704216064000, 19415752042086400000, 225960522265801523200000, 3818732826292045742080000000, 89923520593525093134499840000000
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OFFSET
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0,2
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COMMENT
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sm(x) = sm(x,0) satisfies: Integral_{0}^{sm(x,0)} dy/(1-y^3)^(2/3) = x.
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FORMULA
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a(n) = Product_{k=1..n} (3k-2)*(3k-1)^2 for n>0 with a(0)=1.
E.g.f.: Sum_{n>=0} a(n)*x^(3m)/(3m)! = 1/(1-x^3)^(2/3).
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EXAMPLE
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E.g.f.: 1/(1-x^3)^(2/3) = 1 + 4*x^3/3! + 400*x^6/6! + 179200*x^9/9! +...
E.g.f.: sm^-1(x) = x + 4*x^4/4! + 400*x^7/7! + 179200*x^10/10! +...
sm(x) = x - 4*x^4/4! + 160*x^7/7! - 20800*x^10/10! + 6476800*x^13/13! +...
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PROGRAM
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(PARI) a(n)=prod(k=1, n, (3*k-2)*(3*k-1)^2)
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CROSSREFS
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Cf. A104133, A004988.
Sequence in context: A006237 A116031 A115049 this_sequence A036771 A080321 A125760
Adjacent sequences: A158108 A158109 A158110 this_sequence A158112 A158113 A158114
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 18 2009
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