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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. 0

%I #17 Apr 25 2019 07:13:52

%S 1,3,17,13,481,69,1595,53,64561,19333,-24278897,-4223787,425750784331,

%T 2082755237,-759610365139,-1935668618507,91825384919760257,

%U 3104887811555781,-333936446105117072383,-8039608511659164907,496858217433153687034811,31900258438443561908965,-1108179772136293880993162549,-186044136772398390757763787,167280081459577193334628789960171

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

%C Starting with a top row of Bernoulli numbers, the Akiyama-Tanigawa transform generates further rows as follows:

%C 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66,...

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

%C 17/6, -11/3, 11/10, 6/5, -5/42, -13/7, -7/10, 68/15, 453/110,...

%C 13/2, -143/15, -3/10, 554/105, 365/42, -243/35, -1099/30, 548/165,...

%C 481/30, -277/15, -1171/70, -478/35, 469/6, 1247/7, -6153/22,..

%C 69/2, -73/21, -129/14, -38566/105, -20995/42, 211515/77,...

%C The numerators of the leftmost column define the current sequence.

%C The denominators appear to be the same as A141056.

%H D. Merlini, R. Sprugnoli, M. C. Verri, <a href="https://www.emis.de/journals/INTEGERS/papers/f5/f5.Abstract.html">The Akiyama-Tanigawa Transformation</a>, Integers, 5 (1) (2005) #A05.

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

%t 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 *)

%Y Cf. A174129, A141056, A051049.

%K frac,sign

%O 0,2

%A _Paul Curtz_, Mar 11 2010

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)