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A090765
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).
1
1, 1, 1, 6, 12, 24, 40, 1008, 3360, 362880, 181440, 39916800, 15966720, 6227020800, 32947200, 261534873600, 373621248000, 2845499424768, 88921857024000, 121645100408832000, 1422749712384000, 3005349539512320000, 10218188434341888000, 25852016738884976640000
OFFSET
0,4
COMMENTS
G.f. y=Sum_{k>0} f(n)x^n satisfies y''+y/(1+x)=0. - Michael Somos, Feb 14 2004
REFERENCES
H. K. Wilson, Ordinary Differential Equations, Addison-Wesley, 1971, p. 154.
EXAMPLE
Sequence f(n) begins 0, 1, 0, -1/6, 1/12, -1/24, 1/40, -17/1008, 41/3360, ...
PROG
(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)))
CROSSREFS
Cf. A090295.
Sequence in context: A319127 A367099 A063104 * A199910 A210678 A358508
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Feb 08 2004
STATUS
approved