A246052 Triangle read by rows: denominator of h(n-k)*h(k)/h(n) where h(x) = zeta(2*x)*(4^x-2), 0<=k<=n.

2, 2, 2, 2, 7, 2, 2, 62, 62, 2, 2, 381, 381, 381, 2, 2, 5110, 365, 365, 5110, 2, 2, 1414477, 2828954, 1414477, 2828954, 1414477, 2, 2, 1720110, 49146, 573370, 573370, 49146, 1720110, 2, 2, 16931177, 50793531, 1638501, 118518239, 1638501, 50793531, 16931177, 2

Offset: 0

Author

Peter Luschny, Aug 11 2014

Keywords

• nonn
• frac
• tabl

Comments

Conjecture: A240978(n) divides T(n,k) for k in (1..n-1) and n>=2.

Examples

			             2
            2, 2
          2, 7, 2
        2, 62, 62, 2
    2, 381, 381, 381, 2
2, 5110, 365, 365, 5110, 2
		

Crossrefs

Cf. A246051 (numerators), A240978, A246053.

Programs

Maple

h := x -> Zeta(2*x)*(4^x-2);
A246052 := (n, k) -> denom(h(n-k)*h(k)/h(n));
seq(print(seq(A246052(n, k), k=0..n)), n=0..8);

Sage

h = lambda n: zeta(2*n)*(4^n-2)
A246052 = lambda n, k: (h(n-k)*h(k)/h(n)).denominator()
for n in range(8): [A246052(n, k) for k in (0..n)]