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A090765
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Let f(0) = 0, f(1) = 1 and for n > 1 let f(n) = (-1)*sum((-1)^(n+r)*f(r),r=0..n-2)/(n*(n-1)); sequence gives denominator of f(n).
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1
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1, 1, 1, 6, 12, 24, 40, 1008, 3360, 362880, 181440, 39916800, 15966720, 6227020800, 32947200, 261534873600, 373621248000, 2845499424768, 88921857024000, 121645100408832000, 1422749712384000, 3005349539512320000, 10218188434341888000, 25852016738884976640000
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OFFSET
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0,4
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COMMENTS
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G.f. y=Sum_{k>0} f(n)x^n satisfies y''+y/(1+x)=0. - Michael Somos Feb 14 2004
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REFERENCES
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H. K. Wilson, Ordinary Differential Equations, Addison-Wesley, 1971, p. 154.
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LINKS
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Table of n, a(n) for n=0..23.
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EXAMPLE
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Sequence f(n) begins 0, 1, 0, -1/6, 1/12, -1/24, 1/40, -17/1008, 41/3360, ...
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PROG
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(PARI) a(n)=local(y); if(n<0, 0, y=O(x); for(k=1, n, y=x+intformal(intformal(-y/(1+x)))); denominator(polcoeff(y, n)))
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CROSSREFS
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Cf. A090295.
Sequence in context: A187678 A124509 A063104 * A199910 A210678 A212116
Adjacent sequences: A090762 A090763 A090764 * A090766 A090767 A090768
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane, Feb 08 2004
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STATUS
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approved
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