OFFSET
0,6
COMMENTS
As infinite lower triangular matrices, binomial transform of A134309 = A082137. A134309 * A007318 = A055372. A134309 * [1,2,3,...] = A057711: (1, 2, 6, 16, 40, 96, 224,...).
Triangle read by rows given by [0,0,0,0,0,0,0,0,...] DELTA [1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 20 2007
FORMULA
Triangle, T(0,0) = 1, then for n > 0, n zeros followed by 2^(n-1). Infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in the main diagonal and the rest zeros.
G.f.: (1 - y*x)/(1 - 2*y*x). - Philippe Deléham, Feb 04 2012
Sum_{k=0..n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = 0, 1, 2, 3, 4, 5, 6 respectively. - Philippe Deléham, Feb 04 2012
Diagonal is A011782, other elements are 0. - M. F. Hasler, Mar 29 2022
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
1;
0, 1;
0, 0, 2;
0, 0, 0, 4;
0, 0, 0, 0, 8;
0, 0, 0, 0, 0, 16;
...
MATHEMATICA
Join[{1}, Flatten[Table[Join[{PadRight[{}, n], 2^(n-1)}], {n, 20}]]] (* Harvey P. Dale, Jan 04 2024 *)
PROG
(PARI) A134309(r, c)=if(r==c, 2^max(r-1, 0), 0) \\ M. F. Hasler, Mar 29 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Oct 19 2007
STATUS
approved