A108284 Triangle read by rows, related to A108283.

1, 3, 2, 6, 11, 6, 10, 39, 54, 24, 15, 114, 304, 324, 120, 21, 300, 1384, 2664, 2280, 720, 28, 741, 5598, 17364, 25800, 18360, 5040, 36, 1757, 21054, 99012, 227400, 273720, 166320, 40320, 45, 4052, 75504, 518592, 1728816, 3131400, 3160080, 1673280, 362880, 55, 9162, 262104, 2564892, 11934816, 30523800, 45496080, 39473280, 18506880, 3628800

Offset: 1

Author

Gary W. Adamson, May 30 2005

Keywords

• nonn
• tabl

Examples

			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...).
		

Crossrefs

Cf. A108283.

Programs

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 *)

Formula

n-th row is the inverse binomial transform of n-th column of A108283.

Extensions

More terms from Jean-François Alcover, Sep 13 2016