A258497 Number of words of length 2n such that all letters of the denary 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.

16796, 2735810, 255290156, 17977098425, 1063758951255, 55927419074670, 2700837720153300, 122411464503168984, 5284666028132079380, 219622926821644989478, 8855064908059488718600, 348436223706779520860457, 13441577595226619289460295, 510180504585665885463323546

Offset: 10

Author

Alois P. Heinz, May 31 2015

Keywords

• nonn

Comments

In general, column k>2 of A256117 is asymptotic to (4*(k-1))^n / ((k-2)^2 * (k-2)! * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..650

Crossrefs

Column k=10 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, 10):
seq(a(n), n=10..25);

Formula

a(n) ~ 36^n / (2580480*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015