OFFSET
0,4
COMMENTS
Row sums give A095121.
Triangle T(n,k), 0 <= k <= n, read by rows given by [1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 18 2007
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
Twice Pascal's triangle minus A097806, the pairwise operator.
G.f.: (1-x*y+x^2+x^2*y)/((-1+x+x*y)*(x*y-1)). - R. J. Mathar, Aug 11 2015
EXAMPLE
First few rows of the triangle are:
1;
1, 1;
2, 3, 1;
2, 6, 5, 1;
2, 8, 12, 7, 1;
2, 10, 20, 20, 9, 1;
...
MAPLE
seq(seq( `if`(k=n-1, 2*n-1, `if`(k=n, 1, 2*binomial(n, k))), k=0..n), n=0..12); # G. C. Greubel, Nov 18 2019
MATHEMATICA
Table[If[k==n-1, 2*n-1, If[k==n, 1, 2*Binomial[n, k]]], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 18 2019 *)
PROG
(PARI) T(n, k) = if(k==n-1, 2*n-1, if(k==n, 1, 2*binomial(n, k))); \\ G. C. Greubel, Nov 18 2019
(Magma)
function T(n, k)
if k eq n-1 then return 2*n-1;
elif k eq n then return 1;
else return 2*Binomial(n, k);
end if;
return T;
end function;
[T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 18 2019
(Sage)
@CachedFunction
def T(n, k):
if (k==n-1): return 2*n-1
elif (k==n): return 1
else: return 2*binomial(n, k)
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 18 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 15 2007
EXTENSIONS
Corrected by Philippe Deléham, Dec 17 2007
More terms added and data corrected by G. C. Greubel, Nov 18 2019
STATUS
approved