A258494 Number of words of length 2n such that all letters of the septenary 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.

429, 32032, 1447992, 51647700, 1605746373, 45730269662, 1227377689395, 31600247019120, 789604855530855, 19302666179660304, 464277874912868104, 11032638071392824348, 259801742258903758053, 6076538940891732415102, 141407795779400734204647

Offset: 7

Author

Alois P. Heinz, May 31 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..700

Crossrefs

Column k=7 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, 7):
seq(a(n), n=7..25);

Formula

a(n) ~ 24^n / (3000*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015