A246051 - OEIS

%I #11 Aug 18 2014 16:56:50

%S 1,1,1,1,5,1,1,49,49,1,1,310,343,310,1,1,4191,341,341,4191,1,1,

%T 1162525,2669667,1374230,2669667,1162525,1,1,1414477,46501,562991,

%U 562991,46501,1414477,1,1,13924700,48092218,1613300,117628797,1613300,48092218,13924700,1

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

%e Triangle starts:

%e              1

%e             1, 1

%e           1, 5, 1

%e         1, 49, 49, 1

%e     1, 310, 343, 310, 1

%e 1, 4191, 341, 341, 4191, 1

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

%p A246051 := (n, k) -> h(n-k)*h(k)/h(n);

%p seq(print(seq(numer(A246051(n, k)), k=0..n)), n=0..8);

%o (Sage)

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

%o A246051 = lambda n, k: h(n-k)*h(k)/h(n)

%o for n in range(8): [A246051(n, k).numerator() for k in (0..n)]

%Y Cf. A246052 (denominators).

%K nonn,frac,tabl

%O 0,5

%A _Peter Luschny_, Aug 11 2014