A132096 Numerators of Blandin-Diaz compositional Bernoulli numbers (B^Z)_1,n.

1, -1, 1, 1, 61, -1, -12491, -479, 530629, 54979, 1039405, -4981183, -9055875786121, 908993573959, 288260975797477, 7874837285353, -2255621632465386299, -189404901989770501, -20038592583515962234111, 954329155426992424481, 1731149375200514221429374109

Offset

0,5

Links

Table of n, a(n) for n=0..20.

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

Denominators are A132097.

Cf. A132092-A132099.

Sequence in context: A333523 A249909 A241601 * A051322 A345224 A198189

Adjacent sequences: A132093 A132094 A132095 * A132097 A132098 A132099

Keyword

frac,sign

Author

Jonathan Vos Post, Aug 09 2007

Status

approved