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%I #34 Jan 24 2024 10:07:13
%S 1,-1,1,1,61,-1,-12491,-479,530629,54979,1039405,-4981183,
%T -9055875786121,908993573959,288260975797477,7874837285353,
%U -2255621632465386299,-189404901989770501,-20038592583515962234111,954329155426992424481,1731149375200514221429374109
%N Numerators of Blandin-Diaz compositional Bernoulli numbers (B^Z)_1,n.
%H Hector Blandin and Rafael Diaz, <a href="http://arXiv.org/abs/0708.0809">Compositional Bernoulli numbers</a>, arXiv:0708.0809 [math.CO], 2007-2008, p. 9, 1st table.
%F 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
%F 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
%e 1, -1/4, 1/72, 1/96, 61/21600, -1/640, -12491/5080320, -479/680608.
%t 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 *)
%Y Denominators are A132097.
%Y Cf. A132092-A132099.
%K frac,sign
%O 0,5
%A _Jonathan Vos Post_, Aug 09 2007