A171731 Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).

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, 105, 105, 70, 21, 7, 0, 21, 104, 224, 280, 210, 112, 28, 8, 0, 34, 189, 468, 672, 630, 378, 168, 36, 9, 0, 55, 340, 945, 1560, 1680, 1260, 630, 240, 45, 10, 0

Offset: 0

Author

Philippe Deléham, Dec 16 2009

Keywords

• nonn
• tabl

Comments

Diagonal sums : A112576.

Essentially the same as A094440. - Peter Bala, Jan 06 2015

Examples

			Triangle begins :
0 ;
1,0 ;
1,2,0 ;
2,3,3,0 ;
3,8,6,4,0 ;
5,15,20,10,5,0 ;
...
		

Crossrefs

Cf. A000045, A007318, A094440.

Programs

Mathematica

Flatten[Table[Binomial[n,k]Fibonacci[n-k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Jan 16 2013 *)

Formula

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).