OFFSET
0,3
COMMENTS
From Vaclav Kotesovec, Aug 27 2023: (Start)
a(n)^(1/n^2) tends to 1.1130228... (based on the first 750 terms).
Conjecture: the constant is the same as in A343032. (End)
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
MAPLE
with(LinearAlgebra):
ctln:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
T := proc(n, k)
if n=k then 1
elif irem(n+k, 2)=1 then 0
else Determinant(Matrix((n-k)/2, (i, j)-> ctln(i+j-1+k)))
fi
end:
a:= n-> add(T(n, k), k=0..n):
seq(a(n), n=0..25); # Alois P. Heinz, Feb 15 2011
MATHEMATICA
t[n_, n_] = 1; t[n_, k_] /; Mod[n+k, 2] == 1 = 0; t[n_, k_] := Array[CatalanNumber[#1 + #2 - 1 + k]&, {(n-k)/2, (n-k)/2}] // Det; a[n_] := Sum[t[n, k], {k, 0, n}]; Table[a[n], {n, 0, 22} ] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 15 2011
EXTENSIONS
Corrected and extended by Alois P. Heinz, Feb 15 2011
STATUS
approved