A217940 - OEIS

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

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..45.

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

EXAMPLE

Triangle begins:

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

...

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 *)

CROSSREFS

Right-hand diagonal is A002190.

Sequence in context: A362374 A059812 A077725 * A353000 A372020 A182065

Adjacent sequences: A217937 A217938 A217939 * A217941 A217942 A217943

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 23 2012

EXTENSIONS

More terms from Jean-François Alcover, Feb 13 2013

STATUS

approved