login
A137422
Triangle T(n,k) = A053120(n-1,k) + A053120(n-1,k-1), read by rows.
1
0, 1, 1, 0, 1, 1, -1, -1, 2, 2, 0, -3, -3, 4, 4, 1, 1, -8, -8, 8, 8, 0, 5, 5, -20, -20, 16, 16, -1, -1, 18, 18, -48, -48, 32, 32, 0, -7, -7, 56, 56, -112, -112, 64, 64, 1, 1, -32, -32, 160, 160, -256, -256, 128, 128, 0, 9, 9, -120, -120, 432, 432, -576, -576, 256, 256
OFFSET
0,9
COMMENTS
Row sums are 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
EXAMPLE
Triangle begins
0;
1, 1;
0, 1, 1;
-1, -1, 2, 2;
0, -3, -3, 4, 4;
1, 1, -8, -8, 8, 8;
0, 5, 5, -20, -20, 16, 16;
-1, -1, 18, 18, -48, -48, 32, 32;
0, -7, -7, 56, 56, -112, -112, 64, 64;
1, 1, -32, -32, 160, 160, -256, -256, 128, 128;
0, 9, 9, -120, -120, 432, 432, -576, -576, 256, 256;
MAPLE
A053120 := proc(n, k)
if n <0 or k <0 then
0 ;
else
T(n, x) ;
coeftayl(%, x=0, k) ;
end if;
end proc:
A137422 := proc(n, k)
A053120(n-1, k)+A053120(n-1, k-1)
end proc: # R. J. Mathar, Sep 10 2013
MATHEMATICA
(* Chebyshev A053120 polynomials*) (* Recursive root shifted polynomials*) Q[x, 0] = 1; Q[x, 1] = x + 1; Q[x_, n_] := (x + 1)*ChebyshevT[n - 1, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]
CROSSREFS
Cf. A053120.
Sequence in context: A363532 A207383 A191362 * A139139 A077872 A300453
KEYWORD
tabl,sign
AUTHOR
EXTENSIONS
T(0,0) set to a rationalized 0. - R. J. Mathar, Sep 10 2013
STATUS
approved