A133003 Denominators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n.

1, 4, 72, 48, 21600, 540, 2540160, 483840, 36288000, 896000, 31614105600, 1149603840, 7139902049280000, 2196892938240000, 941525544960000, 15216574464000, 16326052949606400000, 443241256550400000, 11991344662654156800000, 1100420292929126400000

Offset

0,2

Comments

Numerators are A133002.

Links

Daniel Suteu, Table of n, a(n) for n = 0..200

Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, arXiv:0708.0809 [math.CO], 2007-2008, p. 11, 1st table.

Formula

a(n) = denominator(f(n) * n!), where f(0) = 1, f(n) = -Sum_{k=0..n-1} f(k) / ((n-k+1)!)^2. - Daniel Suteu, Feb 23 2018

E.g.f. for fractions: x / (BesselI(0,2*sqrt(x)) - 1). - Ilya Gutkovskiy, Sep 01 2021

Example

1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by Daniel Suteu, Feb 24 2018).

Mathematica

f[0] = 1; f[n_] := f[n] = -Sum[f[k]/((n - k + 1)!)^2, {k, 0, n - 1}]; a[n_] := Denominator[f[n]*n!]; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Feb 25 2018, after Daniel Suteu *)

Crossrefs

Cf. A132092, A132093, A132094, A132095, A132096, A132097, A132098, A132099.

Cf. A133000, A133001, A133002, A133004, A133005.

Sequence in context: A322397 A333543 A262235 * A358293 A340917 A161791

Adjacent sequences: A133000 A133001 A133002 * A133004 A133005 A133006

Keyword

nonn,frac

Author

Jonathan Vos Post, Aug 09 2007

Extensions

Terms beyond a(8) from Daniel Suteu, Feb 24 2018

Status

approved