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A057281 Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057282. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)