[seqfan] Fibinomials

[Ron Hardin]

I was wondering about linear recurrences of powers of series with linear 
recurrences, so I started with F(i)^n

the table of linear recurrence coefficients for power n of a(j]=a(j-1)+a(j-2) 
starts

1 1
2 2 -1
3 6 -3 -1
5 15 -15 -5 1
8 40 -60 -40 8 1
13 104 -260 -260 104 13 -1
21 273 -1092 -1820 1092 273 -21 -1
34 714 -4641 -12376 12376 4641 -714 -34 1
55 1870 -19635 -85085 136136 85085 -19635 -1870 55 1
89 4895 -83215 -582505 1514513 1514513 -582505 -83215 4895 89 -1
144 12816 -352440 -3994320 16776144 27261234 -16776144 -3994320 352440 12816 
-144 -1

so of course I looked up the columns in OEIS, and find that the apparent linear 
recurrence coefficients for column k is row k, if the denominator of the egf 
given there is to be believed.

which I find surprising.  Is it peculiar to F(i)^n?





 rhhardin at mindspring.com
rhhardin at att.net (either)