A174110 Numerators of the image of the Akiyama-Tanigawa transform applied to the second Bernoulli numbers.

1, 2, 1, 2, -1, -1, 1, 4, -3, -25, 5, 1382, -691, -49, 35, 28936, -3617, -131601, 43867, 349222, -1222277, -9399643, 854513, 945456364, -1181820455, -111190339, 76977927, 332492454406, -23749461029, -43079206380025, 8615841276005

Offset: 0

Author

Paul Curtz, Mar 08 2010

Keywords

• sign
• frac

Comments

Start from a row of modified Bernoulli numbers A164555(k)/A027642(k), namely,

1/1, 1/2, 1/6, 0/1, -1/30, 0/1, 1/42, 0/1, -1/30, ... .

Applying the Takiyama-Tanigawa transformation to this sequence results in

1/2, 2/3, 1/2, 2/15, -1/6, -1/7, 1/6, 4/15, -3/10, -25/33, 5/6, ... .

The current sequence contains the numerators of this image of the transform.

Links

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

Programs

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}] // Numerator  (* Jean-François Alcover, Aug 09 2012 *)

Extensions

Values corrected by Lisa Schreiber (lisa.schreiber(AT)uni-jena.de), Jul 14 2010