A258492 Number of words of length 2n such that all letters of the quinary 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.

42, 1485, 34034, 647920, 11187462, 182587701, 2880017910, 44477796451, 677940669900, 10250875770135, 154278143783022, 2316262521915440, 34742240691197182, 521131993897607925, 7822497290908844702, 117554364707534272375, 1769075045150700563052

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..800

Formula

a(n) ~ 16^n / (54*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, 5):
seq(a(n), n=5..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, 5];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A256117.

Sequence in context: A121974 A096048 A215301 * A067638 A155021 A270410

Adjacent sequences: A258489 A258490 A258491 * A258493 A258494 A258495

Keyword

nonn

Author

Alois P. Heinz, May 31 2015

Status

approved