A126770 Unsigned version of A056588.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 16, 7, 1, 1, 12, 53, 53, 12, 1, 1, 20, 166, 318, 166, 20, 1, 1, 33, 492, 1784, 1784, 492, 33, 1, 1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1, 1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1, 1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1

Offset: 0

Author

Philippe Deléham, Feb 17 2007

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  1, 1;
  1, 2, 1;
  1, 4, 4, 1;
  1, 7, 16, 7, 1;
  1, 12, 53, 53, 12, 1;
  1, 20, 166, 318, 166, 20, 1;
  1, 33, 492, 1784, 1784, 492, 33, 1;
  1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1;
  1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1;
  1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1;
		

Crossrefs

Column sequences: A000012, A000071, A056589-91; A056593 (Row sums).

Programs

Mathematica

T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := Fibonacci[(n - k + 1)]*T[ n - 1, k - 1] + Fibonacci[k ]*T[n - 1, k];
Table[T[n, m], {n, 1, 11}, {m, 1, n}] // Flatten (* Roger L. Bagula, Sep 09 2008 *)

Formula

T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,k)=F(n-k+1)*T(n-1,k-1)+F(k+1)*T(n-1,k) where F(n) = A000045(n).