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A057995
Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057280.
3
1, 16, 5, 300, 160, 20, 6840, 4850, 1075, 75, 186120, 159650, 48175, 6100, 275, 5916240, 5846700, 2168650, 379700, 31550, 1000, 215717040, 238437900, 103057800, 22426825, 2605175, 153875, 3625, 8888140800, 10772348400
OFFSET
0,2
COMMENTS
The row polynomials are p(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 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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057280).
EXAMPLE
k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wolfdieter Lang, Sep 13 2000
STATUS
approved