A154218 - OEIS

%I #11 Sep 04 2016 18:44:25

%S 1,1,1,1,2,1,1,4,4,1,1,9,12,9,1,1,20,45,45,20,1,1,48,160,300,160,48,1,

%T 1,117,624,1820,1820,624,117,1,1,294,2457,12012,18200,12012,2457,294,

%U 1,1,748,9996,78897,198016,198016,78897,9996,748,1

%N Modified Fibonomial matrix.

%H G. C. Greubel, <a href="/A154218/b154218.txt">Table of n, a(n) for the first 51 rows</a>

%F T(n,k) = A010048(n,k)*(1 + F(k)*F(n-k)).

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 2, 1,

%e 1, 4, 4, 1,

%e 1, 9, 12, 9, 1,

%e 1, 20, 45, 45, 20, 1.

%p A154218 := proc(n,k)

%p     A010048(n,k)*(1+combinat[fibonacci](k)*combinat[fibonacci](n-k)) ;

%p end proc:

%p seq(seq(A154218(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Feb 05 2015

%t f[n_, k_] := Product[Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; Table[f[n, i]*(1 + Fibonacci[i]*Fibonacci[n - i]), {n, 0, 10}, {i, 0, n}] (* _G. C. Greubel_, Sep 04 2016 *)

%Y Row sums are A154219.

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Jan 05 2009