OFFSET
1,2
FORMULA
n-th row is the inverse binomial transform of n-th column of A108283.
EXAMPLE
Triangle begins:
1;
3, 2;
6, 11, 6;
10, 39, 54, 24;
15, 114, 304, 324, 120; ...
Row 2: (3, 2, 0, 0, 0...), is the inverse binomial transform of column 2 of A108283: (3, 5, 7, 9...).
MATHEMATICA
(* T = A108283 *) T[_, 1] := 1; T[n_, n_] := n*(n + 1)/2; T[n_, k_] := (1 - (n - k + 1)^k*(k^2 - k*n + 1))/(n - k)^2; row[n_] := (TT = Table[T[k, n], {k, n, 2*n - 1}]; Table[Differences[TT, k], {k, 0, n - 1}][[All, 1]]); Table[row[n], {n, 1, 10}] // Flatten (* Jean-François Alcover, Sep 13 2016 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 30 2005
EXTENSIONS
More terms from Jean-François Alcover, Sep 13 2016
STATUS
approved