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

1, 5, 16, 20, 160, 300, 75, 1075, 4850, 6840, 275, 6100, 48175, 159650, 186120, 1000, 31550, 379700, 2168650, 5846700, 5916240, 3625, 153875, 2605175, 22426825, 103057800, 238437900, 215717040, 13125, 720375, 16273875, 195469125

Offset

0,2

Comments

The row polynomials are p(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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057282(k,m).

a(k,0)= A030191(k), k >= 0.

Links

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

Example

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.

Crossrefs

Cf. A000045, A037027, A057995, A057280, A057282.

Sequence in context: A151980 A063612 A269969 * A204920 A168469 A124865

Adjacent sequences: A057278 A057279 A057280 * A057282 A057283 A057284

Keyword

nonn,tabl

Author

Wolfdieter Lang, Sep 13 2000

Status

approved