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%I #41 May 03 2015 09:57:16
%S 1,3,-1,11,-2,1,25,-3,1,0,137,-4,3,1,-1,49,-5,2,1,-1,0,363,-6,5,2,-3,
%T -1,1,761,-7,3,5,-1,-1,1,0,7129,-8,7,5,0,-4,1,1,-1,7381,-9,4,7,1,-1,
%U -1,1,-1,0,83711,-10,9,28,49,-29,-5,8,1,-5,5
%N Numerators of Akiyama-Tanigawa algorithm applied to harmonic numbers, written by antidiagonals.
%C Leading column gives the Bernoulli numbers: A027641(n)/A027642(n). In A051714, A164555 must be written instead of A027641.
%H M. Kaneko, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/KANEKO/AT-kaneko.html">The Akiyama-Tanigawa algorithm for Bernoulli numbers</a>, J. Integer Sequences, Vol 3 (2000), #00.2.9.
%e Numerators of
%e 1, 3/2, 11/6, 25/12,...
%e -1/2, -2/3, -3/4, -4/5,...
%e 1/6, 1/6, 3/20, 2/15,... =A026741(n+1)/A045896(n+1)
%e 0, 1/30, 1/20, 2/35,... =A194531/A193220.
%t t[1, k_] := HarmonicNumber[k]; t[n_, k_] := t[n, k] = k*(t[n-1, k] - t[n-1, k+1]); Table[t[n-k+1, k] // Numerator, {n, 1, 12}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Nov 15 2013 *)
%Y Cf. A051714/A051715, A001008/A002805.
%K sign,frac
%O 0,2
%A _Paul Curtz_, Nov 09 2013
%E More terms from _Jean-François Alcover_, Nov 15 2013