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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.

%I A246052 #11 Aug 18 2014 16:56:09
%S A246052 2,2,2,2,7,2,2,62,62,2,2,381,381,381,2,2,5110,365,365,5110,2,2,
%T A246052 1414477,2828954,1414477,2828954,1414477,2,2,1720110,49146,573370,
%U A246052 573370,49146,1720110,2,2,16931177,50793531,1638501,118518239,1638501,50793531,16931177,2
%N 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.
%C A246052 Conjecture: A240978(n) divides T(n,k) for k in (1..n-1) and n>=2.
%e A246052              2
%e A246052             2, 2
%e A246052           2, 7, 2
%e A246052         2, 62, 62, 2
%e A246052     2, 381, 381, 381, 2
%e A246052 2, 5110, 365, 365, 5110, 2
%p A246052 h := x -> Zeta(2*x)*(4^x-2);
%p A246052 A246052 := (n, k) -> denom(h(n-k)*h(k)/h(n));
%p A246052 seq(print(seq(A246052(n, k), k=0..n)), n=0..8);
%o A246052 (Sage)
%o A246052 h = lambda n: zeta(2*n)*(4^n-2)
%o A246052 A246052 = lambda n, k: (h(n-k)*h(k)/h(n)).denominator()
%o A246052 for n in range(8): [A246052(n, k) for k in (0..n)]
%Y A246052 Cf. A246051 (numerators), A240978, A246053.
%K A246052 nonn,frac,tabl
%O A246052 0,1
%A A246052 _Peter Luschny_, Aug 11 2014