A136256 - OEIS

%I #8 Nov 14 2014 13:40:56

%S 0,-1,1,0,-2,1,-1,2,-3,1,0,0,1,-4,1,3,-2,3,0,-5,1,0,6,-3,8,-1,-6,1,-5,

%T 2,6,-3,15,-2,-7,1,0,-16,5,0,-2,24,-3,-8,1,7,-2,-30,8,-15,0,35,-4,-9,

%U 1,0,30,-7,-40,10,-42,3,48,-5,-10,1,-9,2,75,-15,-35,10,-84,7,63,-6,-11,1

%N Triangle of the coefficients [x^k] of the linear form (x*B_{n-1}(x)-(d/dx) B_n(x)) of the polynomials defined in A137276, 0<=k<=n.

%C Row sums are: 0, 0, -1, -1, -2, 0, 5, 7, 1, -9, -12, -2, 13, 17, 3, -17, -22, -4, 21, 27, 5

%D Harry Hochstadt, Defined differential recursion, The Functions of Mathematical Physics, Dover (New York) (1986), page 49.

%F T(n,k) = A137276(n-1,k-1) - k*A137276(n,k+1). - _R. J. Mathar_, Sep 05 2011

%e 0;

%e -1, 1;

%e 0, -2, 1;

%e -1, 2, -3, 1;

%e 0, 0, 1, -4, 1;

%e 3, -2, 3, 0, -5, 1;

%e 0, 6, -3, 8, -1, -6, 1;

%e -5, 2, 6, -3, 15, -2, -7, 1;

%e 0, -16, 5, 0, -2, 24, -3, -8, 1;

%e 7, -2, -30, 8, -15, 0, 35, -4, -9, 1;

%e 0, 30, -7, -40, 10, -42, 3, 48, -5, -10, 1;

%e -9, 2, 75, -15, -35, 10, -84, 7, 63, -6, -11, 1;

%p B := proc(n,x) option remember; if n < 0 then 0; elif n = 0 then 1; elif n = 1 then x; elif n = 2 then x^2+2 else x*procname(n-1,x)-procname(n-2,x) ; expand(%) ; end if; end proc:

%p BB := proc(n,x) x*B(n-1,x)-diff(B(n,x),x) ; expand(%) ; end proc:

%p A136256 := proc(n,k) coeftayl(BB(n,x),x=0,k) ; end proc:

%p seq(seq(A136256(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Sep 04 2011

%Y Cf. A138034.

%K easy,tabl,sign

%O 0,5

%A _Roger L. Bagula_, Mar 18 2008