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A186232 Row sums of A185249.

%I A186232 #23 Aug 30 2023 03:51:21
%S A186232 1,1,2,3,7,18,58,221,1055,6485,50536,478836,5440177,76190368,
%T A186232 1363369202,31071197441,868697997215,29108097152159,1188937117381254,
%U A186232 61492149340335133,4073478163425582443,335184988593624746984,33170032360612393972748
%N A186232 Row sums of A185249.
%C A186232 From _Vaclav Kotesovec_, Aug 27 2023: (Start)
%C A186232 a(n)^(1/n^2) tends to 1.1130228... (based on the first 750 terms).
%C A186232 Conjecture: the constant is the same as in A343032. (End)
%H A186232 Alois P. Heinz, <a href="/A186232/b186232.txt">Table of n, a(n) for n = 0..100</a>
%p A186232 with(LinearAlgebra):
%p A186232 ctln:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
%p A186232 T := proc(n,k)
%p A186232        if n=k then 1
%p A186232      elif irem(n+k,2)=1 then 0
%p A186232      else Determinant(Matrix((n-k)/2, (i, j)-> ctln(i+j-1+k)))
%p A186232        fi
%p A186232      end:
%p A186232 a:= n-> add(T(n,k), k=0..n):
%p A186232 seq(a(n), n=0..25);  # _Alois P. Heinz_, Feb 15 2011
%t A186232 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_ *)
%K A186232 nonn
%O A186232 0,3
%A A186232 _N. J. A. Sloane_, Feb 15 2011
%E A186232 Corrected and extended by _Alois P. Heinz_, Feb 15 2011