[seqfan] Fibinomials
Ron Hardin
rhhardin at att.net
Wed Apr 6 12:03:50 CEST 2011
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)
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