A258491 Number of words of length 2n such that all letters of the quaternary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word.

14, 300, 4400, 55692, 657370, 7488228, 83752760, 928406556, 10254052556, 113186465340, 1250820198264, 13852280754980, 153813849202674, 1712835575525140, 19129590267619304, 214261857777632700, 2406509409480345364, 27100348605141932540, 305944173898725745944

Offset: 4

Author

Alois P. Heinz, May 31 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..900

Crossrefs

Column k=4 of A256117.

Programs

Maple

A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
      add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
    end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 4):
seq(a(n), n=4..25);

Mathematica

A[n_, k_] := A[n, k] = If[n == 0, 1, (k/n) Sum[Binomial[2n, j] (n - j)* If[j == 0, 1, (k - 1)^j], {j, 0, n - 1}]];
T[n_, k_] := Sum[(-1)^i A[n, k - i]/(i! (k - i)!), {i, 0, k}];
a[n_] := T[n, 4];
a /@ Range[4, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)

Formula

a(n) ~ 12^n / (8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015