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Triangle read by rows: T(n,k) = K(n,1)*I(k,1) - (-1)^(n+k)*I(n,1)* K(k,1), where I(n,x) and K(n,x) are Bessel functions; 0<=k<=n.
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%I #7 Oct 03 2014 13:38:19

%S 0,1,0,2,1,0,9,4,1,0,56,25,6,1,0,457,204,49,8,1,0,4626,2065,496,81,10,

%T 1,0,55969,24984,6001,980,121,12,1,0,788192,351841,84510,13801,1704,

%U 169,14,1,0,12667041,5654440,1358161,221796,27385,2716,225,16,1,0

%N Triangle read by rows: T(n,k) = K(n,1)*I(k,1) - (-1)^(n+k)*I(n,1)* K(k,1), where I(n,x) and K(n,x) are Bessel functions; 0<=k<=n.

%F T(n, 0) = A036243(n-1) for n>=2.

%F T(n, 1) = A036242(n-1) for n>=2.

%e 0;

%e 1, 0;

%e 2, 1, 0;

%e 9, 4, 1, 0;

%e 56, 25, 6, 1, 0;

%e 457, 204, 49, 8, 1, 0;

%e 4626, 2065, 496, 81, 10, 1, 0;

%e 55969, 24984, 6001, 980, 121, 12, 1, 0;

%e 788192, 351841, 84510, 13801, 1704, 169, 14, 1, 0;

%p T := (n, k) -> BesselK(n,1)*BesselI(k,1) - (-1)^(n+k)*BesselI(n,1)* BesselK(k,1);

%p seq(lprint(seq(round(evalf(T(n, k), 99)), k=0..n)), n=0..8);

%o (Sage)

%o T = lambda n, k: bessel_K(n,1)*bessel_I(k,1) - (-1)^(n+k)*bessel_I(n,1)* bessel_K(k,1)

%o for n in range(9): [T(n,k).n().round() for k in (0..n)]

%Y Cf. A036242, A036243.

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Sep 14 2014