|
|
A277363
|
|
Self-convolution of a(n)/4^n gives fibonorials (A003266).
|
|
0
|
|
|
1, 2, 6, 52, 646, 13756, 458780, 24525352, 2094232006, 287618113900, 63647556127412, 22739228686869592, 13126310109506278556, 12250085882856201785816, 18488349380363585366790264, 45134497176992058331312333648, 178246891228174428563552421395782
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Self-convolution of a(n) gives A003266(n)*4^n.
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=0..n} a(k)/4^k * a(n-k)/4^(n-k) = A003266(n).
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n=0, 1, (4^n
*mul((<<0|1>, <1|1>>^i)[1, 2], i=1..n)-
add(a(k)*a(n-k), k=1..n-1))/2)
end:
|
|
MATHEMATICA
|
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}] *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|