A057280 Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057995.

2, 17, 5, 225, 120, 15, 4080, 3050, 700, 50, 94440, 89225, 28625, 3775, 175, 2666880, 3006000, 1208975, 223175, 19225, 625, 89016480, 115299900, 54824650, 12689800, 1537100, 93500, 2250, 3430929600, 4973077800, 2695596850, 737744125

Offset

0,1

Comments

The row polynomials are q(k,x) := sum(a(k,m)*x^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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057995(k,m).

Links

Table of n, a(n) for n=0..31.

Example

k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628.

Crossrefs

Cf. A000045, A037027, A057995.

Sequence in context: A210492 A355555 A370111 * A055677 A362397 A257466

Adjacent sequences: A057277 A057278 A057279 * A057281 A057282 A057283

Keyword

nonn,tabl

Author

Wolfdieter Lang, Sep 13 2000

Status

approved