A090295 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 numerator of f(n).

0, 1, 0, -1, 1, -1, 1, -17, 41, -3359, 1319, -234061, 77141, -25222469, 113513, -775879541, 964485937, -6450310315, 178425130799, -217586071308601, 2282867060899, -4350162631605877, 13410469018835099, -30904230668771778781, 1713176573537644627, -3114541600222419096787

Offset

0,8

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.

Links

Table of n, a(n) for n=0..25.

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)))); numerator(polcoeff(y, n)))

Crossrefs

Cf. A090765.

Sequence in context: A328022 A287308 A355700 * A191457 A191458 A253592

Adjacent sequences: A090292 A090293 A090294 * A090296 A090297 A090298

Keyword

sign,frac

Author

N. J. A. Sloane, Feb 08 2004

Status

approved