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Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).
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%I #12 Jan 07 2015 05:13:26

%S 0,1,0,1,2,0,2,3,3,0,3,8,6,4,0,5,15,20,10,5,0,8,30,45,40,15,6,0,13,56,

%T 105,105,70,21,7,0,21,104,224,280,210,112,28,8,0,34,189,468,672,630,

%U 378,168,36,9,0,55,340,945,1560,1680,1260,630,240,45,10,0

%N Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).

%C Diagonal sums : A112576.

%C Essentially the same as A094440. - _Peter Bala_, Jan 06 2015

%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000045(n), A001906(n), A093131(n), A099453(n-1), A081574(n), A081575(n) for x = 0,1,2,3,4,5 respectively. Sum_{k, 0<=k<=n} T(n,k)*2^(n-k) = A014445(n).

%e Triangle begins :

%e 0 ;

%e 1,0 ;

%e 1,2,0 ;

%e 2,3,3,0 ;

%e 3,8,6,4,0 ;

%e 5,15,20,10,5,0 ;

%e ...

%t Flatten[Table[Binomial[n,k]Fibonacci[n-k],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Jan 16 2013 *)

%Y Cf. A000045, A007318, A094440.

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Dec 16 2009