A174129 -id:A174129 - cp's OEIS frontend

A174182 Numerator of the first column, n-th row of the table of the Akiyama-Tanigawa transform starting from a top row of Bernoulli numbers.

1, 3, 17, 13, 481, 69, 1595, 53, 64561, 19333, -24278897, -4223787, 425750784331, 2082755237, -759610365139, -1935668618507, 91825384919760257, 3104887811555781, -333936446105117072383, -8039608511659164907, 496858217433153687034811, 31900258438443561908965, -1108179772136293880993162549, -186044136772398390757763787, 167280081459577193334628789960171

Offset: 0

Paul Curtz, Mar 11 2010

Starting with a top row of Bernoulli numbers, the Akiyama-Tanigawa transform generates further rows as follows:
  1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66,...
  3/2, -4/3, 1/2, 2/15, -1/6, -1/7, 1/6, 4/15, -3/10, -25/33,..
  17/6, -11/3, 11/10, 6/5, -5/42, -13/7, -7/10, 68/15, 453/110,...
  13/2, -143/15, -3/10, 554/105, 365/42, -243/35, -1099/30, 548/165,...
  481/30, -277/15, -1171/70, -478/35, 469/6, 1247/7, -6153/22,..
  69/2, -73/21, -129/14, -38566/105, -20995/42, 211515/77,...
The numerators of the leftmost column define the current sequence.
The denominators appear to be the same as A141056.

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

Cf. A174129, A141056, A051049.

a[0, k_] := BernoulliB[k]; a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); Table[a[n, 0], {n, 0, 24}] // Numerator (* Jean-François Alcover, Sep 18 2012 *)

(a(n)-A174129(n))/A141056(n) = A000225(n).

cp's OEIS Frontend

A174182 Numerator of the first column, n-th row of the table of the Akiyama-Tanigawa transform starting from a top row of Bernoulli numbers.

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