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A277363 Self-convolution of a(n)/4^n gives fibonorials (A003266).

%I A277363 #8 Oct 12 2016 18:55:13
%S A277363 1,2,6,52,646,13756,458780,24525352,2094232006,287618113900,
%T A277363 63647556127412,22739228686869592,13126310109506278556,
%U A277363 12250085882856201785816,18488349380363585366790264,45134497176992058331312333648,178246891228174428563552421395782
%N A277363 Self-convolution of a(n)/4^n gives fibonorials (A003266).
%C A277363 Self-convolution of a(n) gives A003266(n)*4^n.
%F A277363 Sum_{k=0..n} a(k)/4^k * a(n-k)/4^(n-k) = A003266(n).
%p A277363 a:= proc(n) option remember; `if`(n=0, 1, (4^n
%p A277363       *mul((<<0|1>, <1|1>>^i)[1, 2], i=1..n)-
%p A277363       add(a(k)*a(n-k), k=1..n-1))/2)
%p A277363     end:
%p A277363 seq(a(n), n=0...20);  # _Alois P. Heinz_, Oct 12 2016
%t A277363 With[{n = 20}, Sqrt[Sum[Fibonorial[k] (4 x)^k, {k, 0, n - 1}] + O[x]^n][[3]]] (* before version 10.0 define Fibonorial[n_] := Product[Fibonacci[k], {k, 1, n}] *)
%Y A277363 Cf. A000045, A003266, A277362.
%K A277363 nonn
%O A277363 0,2
%A A277363 _Vladimir Reshetnikov_, Oct 10 2016