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

4,1

Links

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

Formula

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

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 *)

Crossrefs

Column k=4 of A256117.

Sequence in context: A186376 A034834 A276699 * A251220 A205619 A034912

Adjacent sequences: A258488 A258489 A258490 * A258492 A258493 A258494

Keyword

nonn

Author

Alois P. Heinz, May 31 2015

Status

approved