cp's OEIS Frontend

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.

%I A258497 #8 Jun 01 2015 15:40:24
%S A258497 16796,2735810,255290156,17977098425,1063758951255,55927419074670,
%T A258497 2700837720153300,122411464503168984,5284666028132079380,
%U A258497 219622926821644989478,8855064908059488718600,348436223706779520860457,13441577595226619289460295,510180504585665885463323546
%N 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.
%C A258497 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
%H A258497 Alois P. Heinz, <a href="/A258497/b258497.txt">Table of n, a(n) for n = 10..650</a>
%F A258497 a(n) ~ 36^n / (2580480*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 01 2015
%p A258497 A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
%p A258497       add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
%p A258497     end:
%p A258497 T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
%p A258497 a:= n-> T(n, 10):
%p A258497 seq(a(n), n=10..25);
%Y A258497 Column k=10 of A256117.
%K A258497 nonn
%O A258497 10,1
%A A258497 _Alois P. Heinz_, May 31 2015