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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. 5

%I #11 Aug 18 2014 16:56:09

%S 2,2,2,2,7,2,2,62,62,2,2,381,381,381,2,2,5110,365,365,5110,2,2,

%T 1414477,2828954,1414477,2828954,1414477,2,2,1720110,49146,573370,

%U 573370,49146,1720110,2,2,16931177,50793531,1638501,118518239,1638501,50793531,16931177,2

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

%e 2

%e 2, 2

%e 2, 7, 2

%e 2, 62, 62, 2

%e 2, 381, 381, 381, 2

%e 2, 5110, 365, 365, 5110, 2

%p h := x -> Zeta(2*x)*(4^x-2);

%p A246052 := (n, k) -> denom(h(n-k)*h(k)/h(n));

%p seq(print(seq(A246052(n, k), k=0..n)), n=0..8);

%o (Sage)

%o h = lambda n: zeta(2*n)*(4^n-2)

%o A246052 = lambda n, k: (h(n-k)*h(k)/h(n)).denominator()

%o for n in range(8): [A246052(n, k) for k in (0..n)]

%Y Cf. A246051 (numerators), A240978, A246053.

%K nonn,frac,tabl

%O 0,1

%A _Peter Luschny_, Aug 11 2014

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Last modified May 18 02:04 EDT 2024. Contains 372615 sequences. (Running on oeis4.)