A174111 Denominators of the image of a modified Bernoulli-number sequence under the Akiyama-Tanigawa transform.

2, 3, 2, 15, 6, 7, 6, 15, 10, 33, 6, 455, 210, 3, 2, 255, 30, 133, 42, 33, 110, 69, 6, 455, 546, 3, 2, 435, 30, 2387, 462

Offset: 0

Author

Paul Curtz, Mar 08 2010

Keywords

• nonn
• frac

Comments

The image of the sequence A164555(k)/A027642(k), k>=0, under the Takiyama-Tanigawa

transform is

1/2, 2/3, 1/2, 2/15, -1/6, -1/7, 1/6, 4/15, -3/10, -25/33, 5/6, 1382/455, -691/210, -49/3, 35/2, 28936/255, -3617/30, -131601/133, 43867/42, 349222/33, ...

The current sequence contains the denominators of this image.

Links

• D. Merlini, R. Sprugnoli, M. C. Verri, The Akiyama-Tanigawa Transformation, Integers, 5 (1) (2005) #A05

Crossrefs

Cf. A174110 (numerators), A164661.

Programs

Maple

read("transforms3") ;
A174111 := proc(n) Lin := [bernoulli(0),-bernoulli(1),seq(bernoulli(k),k=2..n+1)] ; AKIYATANI(Lin) ; denom(op(n+1,%)) ; end proc:

Mathematica

b[0]=0; b[1]=1; b[2]=1/2; b[n_] := BernoulliB[n-1]; a[0, m_] := b[m+1]; a[n_, m_] := a[n, m] = (m+1)*(a[n-1, m] - a[n-1, m+1]); Table[a[1, m], {m, 0, 30}] // Denominator  (* Jean-François Alcover, Aug 09 2012 *)