A217940 Triangle read by rows: coefficients of polynomials Q_n(x) arising in study of Riemann zeta function.

1, 1, 1, 4, 4, 4, 36, 33, 42, 33, 576, 480, 648, 720, 456, 14400, 10960, 14900, 18780, 17900, 9460, 518400, 362880, 487200, 648240, 730800, 606480, 274800, 25401600, 16465680, 21656040, 29481585, 36149820, 36569190, 26845140, 10643745, 1625702400, 981872640, 1260878080, 1729096320, 2218287120, 2495765440, 2285697120, 1503969600, 530052880

Offset: 1

Author

N. J. A. Sloane, Oct 23 2012

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1
1, 1
4, 4, 4
36, 33, 42, 33
576, 480, 648, 720, 456
14400, 10960, 14900, 18780, 17900, 9460
518400, 362880, 487200, 648240, 730800, 606480, 274800
...
		

Links

• Juan Arias de Reyna, Richard P. Brent and Jan van de Lune, On the sign of the real part of the Riemann zeta-function, arXiv preprint arXiv:1205.4423, 2012

Crossrefs

Right-hand diagonal is A002190.

Programs

Mathematica

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 *)

Extensions

More terms from Jean-François Alcover, Feb 13 2013