A136256 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.

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

Offset

0,5

Comments

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

References

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

Links

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

Formula

T(n,k) = A137276(n-1,k-1) - k*A137276(n,k+1). - R. J. Mathar, Sep 05 2011

Example

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

Maple

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:
BB := proc(n, x) x*B(n-1, x)-diff(B(n, x), x) ; expand(%) ; end proc:
A136256 := proc(n, k) coeftayl(BB(n, x), x=0, k) ; end proc:
seq(seq(A136256(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Sep 04 2011

Crossrefs

Cf. A138034.

Sequence in context: A329221 A177858 A166967 * A283440 A337319 A159864

Adjacent sequences: A136253 A136254 A136255 * A136257 A136258 A136259

Keyword

easy,tabl,sign

Author

Roger L. Bagula, Mar 18 2008

Status

approved