A132097 Denominators of Blandin-Diaz compositional Bernoulli numbers (B^Z)_1,n.

1, 4, 72, 96, 21600, 640, 5080320, 580608, 326592000, 20736000, 2529128448, 1094860800, 1298164008960000, 399435079680000, 11298306539520000, 231760134144000, 48978158848819200000, 768284844687360000, 81541143706048266240000, 1009797445276139520000, 467359502609929273344000000

Offset

0,2

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

a(n) = denominator(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}]]; Denominator[A[[All, 1]]] (* Mats Granvik, Feb 03 2018 *)

Crossrefs

Numerators are A132096.

Cf. A132092-A132099.

Sequence in context: A358293 A340917 A161791 * A128062 A336253 A227248

Adjacent sequences: A132094 A132095 A132096 * A132098 A132099 A132100

Keyword

frac,nonn

Author

Jonathan Vos Post, Aug 09 2007

Status

approved