%I #13 Nov 14 2019 09:42:17
%S 1,2,1,3,4,2,4,9,9,3,5,16,24,16,5,6,25,50,50,30,8,7,36,90,120,105,54,
%T 13,8,49,147,245,280,210,98,21,9,64,224,448,630,616,420,176,34,10,81,
%U 324,756,1260,1512,1344,828,315,55,11,100,450,1200,2310,3276,3570,2880,1620
%N Triangle read by rows: T(n,k) = Fibonacci(k+1)*binomial(n,k) + (k+1)*binomial(n,k+1) (0 <= k <= n).
%C Binomial transform of the bidiagonal matrix with the Fibonacci numbers (1, 1, 2, 3, 5, 8, ...) in the main diagonal and (1, 2, 3, ...) in the subdiagonal.
%C Sum of terms in row n = n*2^(n-1) + Fibonacci(2n+1) (A081663).
%e First few rows of the triangle:
%e 1;
%e 2, 1;
%e 3, 4, 2;
%e 4, 9, 9, 3;
%e 5, 16, 24, 16, 5;
%e 6, 25, 50, 50, 30, 8;
%e 7, 36, 90, 120, 105, 54, 13;
%e 8, 49, 147, 245, 280, 210, 98, 21;
%e ...
%p with(combinat): T:=(n,k)->binomial(n,k)*fibonacci(k+1)+(k+1)*binomial(n,k+1): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
%Y Cf. A081663, A081659.
%Y Cf. A000045.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Nov 20 2006
%E Edited by _N. J. A. Sloane_, Nov 29 2006