A246656 Triangle read by rows: T(n, k) is the coefficient of x^k of the polynomial p_n(x) representing the n-th diagonal of A246654.

0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 0, 0, 3, 0, -1, 0, 1, 0, 1, 8, 5, -5, 0, 3, 1, 0, 0, -18, 0, 29, 0, -8, 0, 1, 0, 1, -80, -13, 121, 29, -35, -7, 4, 1, 0, 0, 357, 0, -513, 0, 182, 0, -22, 0, 1, 0, 1, 1865, 344, -2686, -484, 945, 175, -114, -21, 5, 1, 0

Offset

0,18

Links

Table of n, a(n) for n=0..77.

Example

The first few polynomials and their coefficients:
             0;               0;
            1, 0;             1;
          0, 1, 0;            x;
         1, 1, 1, 0;          x*(x+1)+1;
       0, 1, 0, 1, 0;         x*(x^2+1);
      1, 1, 2, 2, 1, 0;       x*(x+1)*(x^2+x+1)+1;
    0, 3, 0, -1, 0, 1, 0;     x*(x^4-x^2+3);
  1, 8, 5, -5, 0, 3, 1, 0;    x*(x+1)*(x^4+2*x^3-2*x^2-3*x+8)+1;
0,-18, 0, 29, 0, -8, 0, 1,0;  x*(x^6-8*x^4+29*x^2-18);
The values of some polynomials:
------------------------------------------------
     n:    -4    -3   -2  -1   0   1    2     3
------------------------------------------------
p_0(n):     0,    0,   0,  0,  0,  0,   0,    0,   A000004
p_1(n):     1,    1,   1,  1,  1,  1,   1,    1,   A000012
p_2(n):    -4,   -3,  -2, -1,  0,  1,   2,    3,   A001477
p_3(n):    13,    7,   3,  1,  1,  3,   7,   13,   A002061
p_4(n):   -68,  -30, -10, -2,  0,  2,  10,   30,   A034262
p_5(n):   157,   43,   7,  1,  1,  7,  43,  157,
p_6(n):  -972, -225, -30, -3,  0,  3,  30,  225,

Maple

with(Student[NumericalAnalysis]):
poly := proc(n) local B; if n = 0 then return 0 fi;
B := (n, k) -> round(evalf(2*(BesselK(n, 2)*BesselI(k, 2)
-(-1)^(n+k)*BesselI(n, 2)*BesselK(k, 2)), 64));
[seq([k+iquo(n, 2), B(k+n, k)], k=-iquo(n, 2)..n-1)];
PolynomialInterpolation(%, independentvar=x);
expand(Interpolant(%)) end:
A246656_row := n -> seq(coeff(poly(n), x, j), j=0..n);
seq(print(A246656_row(n)), n=0..11);

Crossrefs

Cf. A246654, A001477, A002061, A034262.

Sequence in context: A137566 A258277 A122865 * A352988 A334493 A074080

Adjacent sequences: A246653 A246654 A246655 * A246657 A246658 A246659

Keyword

tabl,sign

Author

Peter Luschny, Sep 13 2014

Status

approved