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%I #8 Jun 14 2015 14:48:51
%S 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,
%T 1,33,492,1784,1784,492,33,1,1,54,1413,9288,17840,9288,1413,54,1,1,88,
%U 3960,46233,163504,163504,46233,3960,88,1,1,143,10912,221859,1418549
%N Unsigned version of A056588.
%F 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)=Fibonacci(n)=A000045(n).
%F T(n,k)=Fibonacci[(n - k + 1)]*A(n - 1, k - 1) + Fibonacci[k ]*A(n - 1, k). - _Roger L. Bagula_, Sep 09 2008
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 4, 1;
%e 1, 7, 16, 7, 1;
%e 1, 12, 53, 53, 12, 1;
%e 1, 20, 166, 318, 166, 20, 1;
%e 1, 33, 492, 1784, 1784, 492, 33, 1;
%e 1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1;
%e 1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1;
%e 1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1;
%t 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[Table[T[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - _Roger L. Bagula_, Sep 09 2008
%Y Column sequences :A000012, A000071, A056589-91; A056593 (Row sums).
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Feb 17 2007
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