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A246658 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.

%I A246658 #7 Oct 03 2014 13:38:19
%S A246658 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 A246658 1,0,55969,24984,6001,980,121,12,1,0,788192,351841,84510,13801,1704,
%U A246658 169,14,1,0,12667041,5654440,1358161,221796,27385,2716,225,16,1,0
%N A246658 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 A246658 T(n, 0) = A036243(n-1) for n>=2.
%F A246658 T(n, 1) = A036242(n-1) for n>=2.
%e A246658      0;
%e A246658      1,      0;
%e A246658      2,      1,     0;
%e A246658      9,      4,     1,     0;
%e A246658     56,     25,     6,     1,    0;
%e A246658    457,    204,    49,     8,    1,   0;
%e A246658   4626,   2065,   496,    81,   10,   1,  0;
%e A246658 55969,  24984,  6001,   980,  121,  12,  1, 0;
%e A246658 788192, 351841, 84510, 13801, 1704, 169, 14, 1, 0;
%p A246658 T := (n, k) -> BesselK(n,1)*BesselI(k,1) - (-1)^(n+k)*BesselI(n,1)* BesselK(k,1);
%p A246658 seq(lprint(seq(round(evalf(T(n, k), 99)), k=0..n)), n=0..8);
%o A246658 (Sage)
%o A246658 T = lambda n, k: bessel_K(n,1)*bessel_I(k,1) - (-1)^(n+k)*bessel_I(n,1)* bessel_K(k,1)
%o A246658 for n in range(9): [T(n,k).n().round() for k in (0..n)]
%Y A246658 Cf. A036242, A036243.
%K A246658 nonn,tabl
%O A246658 0,4
%A A246658 _Peter Luschny_, Sep 14 2014