A057282 Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057281.

2, 5, 17, 15, 120, 225, 50, 700, 3050, 4080, 175, 3775, 28625, 89225, 94440, 625, 19225, 223175, 1208975, 3006000, 2666880, 2250, 93500, 1537100, 12689800, 54824650, 115299900, 89016480, 8125, 438250, 9670750, 112454500, 737744125

Offset: 1

Author

Wolfdieter Lang, Sep 13 2000

Keywords

• nonn
• tabl

Comments

The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..

The k-th convolution of F0(n) := A000045(n+1), n >= 0, (Fibonacci numbers starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^k), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A057281(k,m).

a(k,0)= A020876(k), k >= 0.

Examples

			k=2: F2(n)=((5*n^2+21*n+16)*F(n+2)+(5*n^2+27*n+34)*F(n+1))/50, F(n) := A000045(n); see A001628.
2; 5,17; 15,120,225; 50,700,3050,4080; 175,3775,28625,89225,94440; ...
		

Crossrefs

Cf. A000045, A037027, A057995, A057280, A057281.

Row sums: A151615.