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%I #13 Oct 20 2014 17:15:18
%S 1,1,1,4,4,4,36,33,42,33,576,480,648,720,456,14400,10960,14900,18780,
%T 17900,9460,518400,362880,487200,648240,730800,606480,274800,25401600,
%U 16465680,21656040,29481585,36149820,36569190,26845140,10643745,1625702400,981872640,1260878080,1729096320,2218287120,2495765440,2285697120,1503969600,530052880
%N Triangle read by rows: coefficients of polynomials Q_n(x) arising in study of Riemann zeta function.
%H Juan Arias de Reyna, Richard P. Brent and Jan van de Lune, <a href="http://arxiv.org/abs/1205.4423">On the sign of the real part of the Riemann zeta-function</a>, arXiv preprint arXiv:1205.4423, 2012
%e Triangle begins:
%e 1
%e 1, 1
%e 4, 4, 4
%e 36, 33, 42, 33
%e 576, 480, 648, 720, 456
%e 14400, 10960, 14900, 18780, 17900, 9460
%e 518400, 362880, 487200, 648240, 730800, 606480, 274800
%e ...
%t Clear[q]; q[n_, 1] := (n-1)!^2; q[n_, k_] := q[n, k] = Sum[ Binomial[n-1, j]*Binomial[n-1, j+1]* Sum[q[j+1, r]*q[n-j-1, k-r], {r, Max[1, -n+j+k+1], Min[j+1, k-1]}], {j, 0, n-2}]; Table[q[n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 13 2013 *)
%Y Right-hand diagonal is A002190.
%K nonn,tabl
%O 1,4
%A _N. J. A. Sloane_, Oct 23 2012
%E More terms from _Jean-François Alcover_, Feb 13 2013
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