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%I #22 Apr 25 2019 07:09:41
%S 1,30,20,35,84,84,120,495,55,286,1092,455,280,2040,816,969,855,1330,
%T 1540,5313,1012,2300,7800,2925,819,10962,4060,4495,7440,5456,5984,
%U 19635,1785,7770,25308,9139,4940
%N Denominators of the fourth row of Akiyama-Tanigawa algorithm leading to Bernoulli numbers A164555(n)/A027642(n).
%C Denominators of row k=3 of the table in A051714.
%H M. Kaneko, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/KANEKO/AT-kaneko.html">The Akiyama-Tanigawa algorithm for Bernoulli numbers</a>, J. Integer Sequences, 3 (2000), #00.2.9.
%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.
%e The third row is 0, 1/30, 1/20, 2/35, 5/84, 5/84, 7/120, 28/495, 3/55, 15/286, 55/1092, 22/455, 13/280, ...
%p read("transforms3");
%p L := [seq(1/n,n=1..40)] ;
%p L1 := AKIYATANI(L) ; L2 := AKIYATANI(L1) ; L3 := AKIYATANI(L2) ;
%p apply(denom,%) ; # _R. J. Mathar_, Aug 20 2011
%t a[0, k_] := 1/(k+1); a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); Table[a[3, k], {k, 0, 36}] // Denominator (* _Jean-François Alcover_, Sep 18 2012 *)
%Y Cf. A194531 (numerators).
%K nonn,frac
%O 0,2
%A _Paul Curtz_, Jul 18 2011
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