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1, 1, 2, 3, 7, 18, 58, 221, 1055, 6485, 50536, 478836, 5440177, 76190368, 1363369202, 31071197441, 868697997215, 29108097152159, 1188937117381254, 61492149340335133, 4073478163425582443, 335184988593624746984, 33170032360612393972748
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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)
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LINKS
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MAPLE
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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):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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