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%I #9 Nov 11 2022 13:17:41
%S 1,1,1,1,3,1,1,6,6,1,1,10,20,10,1,1,15,50,50,15,1,1,21,105,173,105,21,
%T 1,1,28,196,476,476,196,28,1,1,36,336,1120,1643,1120,336,36,1,1,45,
%U 540,2352,4707,4707,2352,540,45,1,1,55,825,4530,11775,16040,11775,4530,825,55,1
%N A Fibonacci-Pascal triangle.
%C Row sums are A162746.
%H Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Barry4/barry142.html">On a Generalization of the Narayana Triangle</a>, J. Int. Seq. 14 (2011) # 11.4.5.
%F T(n,k) = Sum_{j=0..n} C(n,j)*C(n-j,2(k-j))*Fibonacci(k-j+1).
%e Triangle begins
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 6, 6, 1;
%e 1, 10, 20, 10, 1;
%e 1, 15, 50, 50, 15, 1;
%e 1, 21, 105, 173, 105, 21, 1;
%e 1, 28, 196, 476, 476, 196, 28, 1;
%e 1, 36, 336, 1120, 1643, 1120, 336, 36, 1;
%e 1, 45, 540, 2352, 4707, 4707, 2352, 540, 45, 1;
%o (PARI) T(n,k)=sum(j=0, n, binomial(n,j)*binomial(n-j,2*(k-j))*fibonacci(k-j+1));
%o row(n) = vector(n+1, k, T(n, k-1)); \\ _Michel Marcus_, Nov 11 2022
%Y Cf. A000045.
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Jul 12 2009
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