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A057280 Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057995. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A144212 A186683 A210492 * A055677 A257466 A226291

Adjacent sequences:  A057277 A057278 A057279 * A057281 A057282 A057283

KEYWORD

nonn,tabl

AUTHOR

Wolfdieter Lang, Sep 13 2000

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)