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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. 2

%I

%S 16796,2735810,255290156,17977098425,1063758951255,55927419074670,

%T 2700837720153300,122411464503168984,5284666028132079380,

%U 219622926821644989478,8855064908059488718600,348436223706779520860457,13441577595226619289460295,510180504585665885463323546

%N 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 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 Alois P. Heinz, <a href="/A258497/b258497.txt">Table of n, a(n) for n = 10..650</a>

%F a(n) ~ 36^n / (2580480*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 01 2015

%p A:= proc(n, k) option remember; `if`(n=0, 1, k/n*

%p add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))

%p end:

%p T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):

%p a:= n-> T(n, 10):

%p seq(a(n), n=10..25);

%Y Column k=10 of A256117.

%K nonn

%O 10,1

%A _Alois P. Heinz_, May 31 2015

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)