A186232 Row sums of A185249.

1, 1, 2, 3, 7, 18, 58, 221, 1055, 6485, 50536, 478836, 5440177, 76190368, 1363369202, 31071197441, 868697997215, 29108097152159, 1188937117381254, 61492149340335133, 4073478163425582443, 335184988593624746984, 33170032360612393972748

Offset: 0

Author

N. J. A. Sloane, Feb 15 2011

Keywords

• nonn

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

Programs

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 *)

Extensions

Corrected and extended by Alois P. Heinz, Feb 15 2011