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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.

%I A246656 #12 Sep 16 2014 05:47:32
%S A246656 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,
%T A246656 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,
%U A246656 -513,0,182,0,-22,0,1,0,1,1865,344,-2686,-484,945,175,-114,-21,5,1,0
%N 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.
%e A246656 The first few polynomials and their coefficients:
%e A246656              0;               0;
%e A246656             1, 0;             1;
%e A246656           0, 1, 0;            x;
%e A246656          1, 1, 1, 0;          x*(x+1)+1;
%e A246656        0, 1, 0, 1, 0;         x*(x^2+1);
%e A246656       1, 1, 2, 2, 1, 0;       x*(x+1)*(x^2+x+1)+1;
%e A246656     0, 3, 0, -1, 0, 1, 0;     x*(x^4-x^2+3);
%e A246656   1, 8, 5, -5, 0, 3, 1, 0;    x*(x+1)*(x^4+2*x^3-2*x^2-3*x+8)+1;
%e A246656 0,-18, 0, 29, 0, -8, 0, 1,0;  x*(x^6-8*x^4+29*x^2-18);
%e A246656 The values of some polynomials:
%e A246656 ------------------------------------------------
%e A246656      n:    -4    -3   -2  -1   0   1    2     3
%e A246656 ------------------------------------------------
%e A246656 p_0(n):     0,    0,   0,  0,  0,  0,   0,    0,   A000004
%e A246656 p_1(n):     1,    1,   1,  1,  1,  1,   1,    1,   A000012
%e A246656 p_2(n):    -4,   -3,  -2, -1,  0,  1,   2,    3,   A001477
%e A246656 p_3(n):    13,    7,   3,  1,  1,  3,   7,   13,   A002061
%e A246656 p_4(n):   -68,  -30, -10, -2,  0,  2,  10,   30,   A034262
%e A246656 p_5(n):   157,   43,   7,  1,  1,  7,  43,  157,
%e A246656 p_6(n):  -972, -225, -30, -3,  0,  3,  30,  225,
%p A246656 with(Student[NumericalAnalysis]):
%p A246656 poly := proc(n) local B; if n = 0 then return 0 fi;
%p A246656 B := (n,k) -> round(evalf(2*(BesselK(n,2)*BesselI(k,2)
%p A246656 -(-1)^(n+k)*BesselI(n,2)*BesselK(k,2)),64));
%p A246656 [seq([k+iquo(n,2),B(k+n,k)], k=-iquo(n,2)..n-1)];
%p A246656 PolynomialInterpolation(%, independentvar=x);
%p A246656 expand(Interpolant(%)) end:
%p A246656 A246656_row := n -> seq(coeff(poly(n),x,j), j=0..n);
%p A246656 seq(print(A246656_row(n)), n=0..11);
%Y A246656 Cf. A246654, A001477, A002061, A034262.
%K A246656 tabl,sign
%O A246656 0,18
%A A246656 _Peter Luschny_, Sep 13 2014