%I A081576
%S A081576 0,0,1,0,1,1,0,1,3,2,0,1,5,8,3,0,1,7,20,21,5,0,1,9,38,75,55,8,0,1,11,62,
%T A081576 189,275,144,13,0,1,13,92,387,905,1000,377,21,0,1,15,128,693,2305,4256,
%U A081576 3625,987,34,0,1,17,170,1131,4955,13392,19837,13125,2584,55
%N A081576 Square array of binomial transforms of Fibonacci numbers, read by antidiagonals.
%C A081576 Rows include A000045, A001906, A030191, A081573, A081574, A081575. Row 
               are solutions of the recurrence a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2),
               a(0)=0,a(1)=1.
%F A081576 Rows are successive binomial transforms of F(n). T(n, k)=((sqrt(5)/2 
               + (2*k + 1)/2)^n - ((2*k + 1)/2 - sqrt(5)/2)^n)/sqrt(5)
%e A081576 Rows start
%e A081576 0 1 1 2 3 5 ...
%e A081576 0 1 3 8 21 55 ...
%e A081576 0 1 5 20 75 275 ...
%e A081576 0 1 7 38 189 905 ...
%e A081576 0 1 9 62 387 2305 ...
%Y A081576 Sequence in context: A151844 A008783 A139144 this_sequence A054654 A154477 
               A142071
%Y A081576 Adjacent sequences: A081573 A081574 A081575 this_sequence A081577 A081578 
               A081579
%K A081576 easy,nonn,tabl
%O A081576 0,9
%A A081576 Paul Barry (pbarry(AT)wit.ie), Mar 22 2003