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A226057
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E.g.f. A(x) satisfies: A(x)^2 = -x*log(1-A(x)) where A(x) = Sum_{n>=1} a(n)*x^n/n!^2.
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0
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1, 2, 21, 504, 21380, 1405800, 132139140, 16801276800, 2775758497344, 577868994460800, 147973478687496000, 45703277816543424000, 16753246307626306832640, 7190163806348621417679360, 3571395525388698501285792000
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = n!^2*(n-1)!/(2*n-1)! * {[x^(n-1)] Product_{k=0..2*n-2} (1+k*x)}.
a(n) = n!^2*(n-1)!/(2*n-1)! * A129505(n), where A129505(n) = number of permutations of 2n-1 objects with exactly n cycles.
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EXAMPLE
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E.g.f.: A(x) = x + 2*x^2/2!^2 + 21*x^3/3!^2 + 504*x^4/4!^2 + 21380*x^5/5!^2 +...
where
A(x)^2 = 2*x^2/2! + 6*x^3/3! + 34*x^4/4! + 280*x^5/5! + 3013*x^6/6! + 39963*x^7/7! + 629541*x^8/8! +...
and
-log(1-A(x)) = 2*x/2! + 6*x^2/3! + 34*x^3/4! + 280*x^4/5! + 3013*x^5/6! +...
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PROG
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(PARI) {a(n)=polcoeff(prod(k=0, 2*n-2, 1+k*x), n-1)*n!^2*(n-1)!/(2*n-1)!}
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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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