OFFSET
0,5
LINKS
Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, arXiv:0708.0809 [math.CO], 2007-2008, p. 9, 1st table.
FORMULA
This sequence appears to be the numerators of the first column in the matrix inverse of the lower triangular matrix: If n >= k then binomial(n-1,k-1)/(n-k+1)^2, otherwise 0. - Mats Granvik, Feb 05 2018
a(n) = numerator(f(n)), where f(0) = 1, f(n) = -Sum_{k=0..n-1} f(k) * binomial(n,k) / (n-k+1)^2. - Daniel Suteu, Feb 23 2018
EXAMPLE
1, -1/4, 1/72, 1/96, 61/21600, -1/640, -12491/5080320, -479/680608.
MATHEMATICA
nn = 21; A = Inverse[Table[Table[If[n >= k, Binomial[n - 1, k - 1]/(n - k + 1)^2, 0], {k, 1, nn}], {n, 1, nn}]]; Numerator[A[[All, 1]]] (* Mats Granvik, Feb 05 2018 *)
CROSSREFS
KEYWORD
frac,sign
AUTHOR
Jonathan Vos Post, Aug 09 2007
STATUS
approved