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.

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, 1, 0, 55969, 24984, 6001, 980, 121, 12, 1, 0, 788192, 351841, 84510, 13801, 1704, 169, 14, 1, 0, 12667041, 5654440, 1358161, 221796, 27385, 2716, 225, 16, 1, 0

Offset: 0

Author

Peter Luschny, Sep 14 2014

Keywords

• nonn
• tabl

Examples

			     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,   1,  0;
55969,  24984,  6001,   980,  121,  12,  1, 0;
788192, 351841, 84510, 13801, 1704, 169, 14, 1, 0;
		

Crossrefs

Cf. A036242, A036243.

Programs

Maple

T := (n, k) -> BesselK(n,1)*BesselI(k,1) - (-1)^(n+k)*BesselI(n,1)* BesselK(k,1);
seq(lprint(seq(round(evalf(T(n, k), 99)), k=0..n)), n=0..8);

Sage

T = lambda n, k: bessel_K(n,1)*bessel_I(k,1) - (-1)^(n+k)*bessel_I(n,1)* bessel_K(k,1)
for n in range(9): [T(n,k).n().round() for k in (0..n)]

Formula

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

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