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

0,3

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

Sequence in context: A005248 A032102 A100388 * A160181 A096203 A328430

Adjacent sequences: A186229 A186230 A186231 * A186233 A186234 A186235

Keyword

nonn

Author

N. J. A. Sloane, Feb 15 2011

Extensions

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

Status

approved